10th Class Mathematics Coordinate Geometry Question Bank

done Co-ordinate Geometry Total Questions - 55

• question_answer1)
  A plane is divided into four equal parts by the coordinate axes. What is each part called?
  A)
   Quadrant                            done clear
  B)
   Segment done clear
  C)
   Sector                  done clear
  D)
          Half-plane done clear
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• question_answer2)
  In which quadrant(s) is abscissa positive?
  A)
   I only                    done clear
  B)
          III only done clear
  C)
   I and IV only      done clear
  D)
          II and III only done clear
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• question_answer3)
  In which quadrant (s) is ordinate positive?
  A)
   II only                   done clear
  B)
          I and II only done clear
  C)
   I and IV only      done clear
  D)
          III and IV only done clear
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• question_answer4)
  A point P is at a distance of 3 units from the Y-axis and 4 units from the X-axis. If P is in quadrant I, what are the co-ordinates of P?
  A)
   (-3, 4)                   done clear
  B)
          (3, -4) done clear
  C)
   (-3, -4)                 done clear
  D)
          (3, 4) done clear
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• question_answer5)
  What is the area of a triangle whose vertices are A(5, -1), B(3,8) and C(-4,2)7
  A)
   28 sq units          done clear
  B)
          42.5 sq units done clear
  C)
   35 sq units          done clear
  D)
          37.5 sq units done clear
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• question_answer6)
  What is the distance between the points\[x(a,b)\] and\[y(-a,-b)\]?
  A)
   \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]  done clear
  B)
          \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] done clear
  C)
   \[2{{a}^{2}}+{{b}^{2}}\]                done clear
  D)
          \[2{{a}^{2}}+2{{b}^{2}}\] done clear
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• question_answer7)
  What is the area of the rhombus formed by (3, 0), (4, 5), (-1, 4) and (-2, -1) as vertices?
  A)
   16 sq. units   done clear
  B)
                          32 sq. units done clear
  C)
   42 sq. units   done clear
  D)
          24 sq. units done clear
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• question_answer8)
  What type of a triangle is formed with points (3, -3), (-3,3) and\[(-3\sqrt{3},-3\sqrt{3})\] as vertices?
  A)
   A scalene triangle done clear
  B)
   An equilateral triangle done clear
  C)
   An isosceles triangle done clear
  D)
   A right triangle done clear
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• question_answer9)
  For what value of 'x' are A(2,3), B(x, y) and C(4,3) the vertices of a right triangle with right angle at A?
  A)
   2                             done clear
  B)
          4 done clear
  C)
   5                             done clear
  D)
          3 done clear
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• question_answer10)
  What are the coordinates of the point X that divides the join of A (7, 4) and B(-3, 6) in the ratio 1 :3?
  A)
   \[\left( \frac{9}{2},\frac{11}{2} \right)\] done clear
  B)
          \[\left( \frac{9}{2},\frac{5}{2} \right)\] done clear
  C)
   \[\left( \frac{9}{2},\frac{9}{2} \right)\]   done clear
  D)
          \[\left( \frac{2}{9},\frac{2}{9} \right)\] done clear
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• question_answer11)
  What are the coordinates of the centroid of the triangle whose vertices are (6,9), (5,7) and (4,10)?
  A)
   (3, 9)                                     done clear
  B)
   (4, 9) done clear
  C)
   (6, 8)                     done clear
  D)
          \[\left( 5,8\frac{2}{3} \right)\] done clear
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• question_answer12)
  For what value of 'm' are the points (5,5), (m, 7) and (8,8) collinear?
  A)
   6                                             done clear
  B)
   7 done clear
  C)
   8                             done clear
  D)
          5 done clear
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• question_answer13)
  Find the centroid of the triangle whose vertices are (-3, 2), (1,5) and (11, -19).
  A)
   (3, 4)                                     done clear
  B)
   (3, -4) done clear
  C)
   (-3, -4)                 done clear
  D)
          (-3, 4) done clear
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• question_answer14)
  For what values of 'p' and 'q' are (-2, -1), (p, 0), (4, q) and (1, 2) the vertices of a parallelogram?
  A)
   \[\text{p}=-\text{1},\text{q}=-\text{3}\] done clear
  B)
   \[\text{p}=\text{2},\text{q}=\text{3}\] done clear
  C)
   \[\text{p}=\text{1},\text{q}=\text{3}\] done clear
  D)
   \[\text{p}=-\text{1},\text{q}=\text{3}\] done clear
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• question_answer15)
  A What is the ratio in which P(2,5) divides the line joining the points (8, 2) and (-6.9)?
  A)
   3:4                         done clear
  B)
          1:3 done clear
  C)
   4:3                         done clear
  D)
          1:4 done clear
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• question_answer16)
  If P (6, 7), Q (2, 3) and R (4, -2) are the vertices of a triangle, which of the following is not a point contained in it?
  A)
   (4, 3)                     done clear
  B)
          (3, 3) done clear
  C)
   (4, 2)                     done clear
  D)
          (6, 1) done clear
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• question_answer17)
  Identify the nearest point from the origin.
  A)
   (2,-3)                    done clear
  B)
          (5, 0) done clear
  C)
   (2,-1)                    done clear
  D)
          (1, 3) done clear
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• question_answer18)
  Find the value of 'p' if the distance between the points (8, p) and (4, 3) is 5.
  A)
   6                             done clear
  B)
          0 done clear
  C)
   Both [a] and [b]  done clear
  D)
         1 done clear
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• question_answer19)
  Find the number of points on X-axis which are at a distance 'c' units (c < 3) from (2, 3).
  A)
   1                             done clear
  B)
          2 done clear
  C)
   0                             done clear
  D)
          3 done clear
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• question_answer20)
  Find a point on the X-axis which is equidistant from the points (5, 4) and (-3, 3).
  A)
   (2, 0)                     done clear
  B)
          (0, 3) done clear
  C)
   (-2, 2)                   done clear
  D)
          (3, 0) done clear
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• question_answer21)
  Find the area of the triangle whose vertices are\[(\text{a},\text{b}+\text{c}),(\text{a},\text{b}-\text{c})\] and\[(-\text{a},\text{c})\].
  A)
   2ac                        done clear
  B)
          2bc done clear
  C)
   \[\text{b(a}+\text{c)}\]               done clear
  D)
          \[\text{c(a}-\text{b)}\] done clear
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• question_answer22)
  P (3,4);Q (7,7) are collinear with the point R. Find the coordinates of R.
  A)
   (5, 2)                     done clear
  B)
          (-5,2) done clear
  C)
   (-5,-2)                  done clear
  D)
          (5,-2) done clear
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• question_answer23)
  A line is of length 10 units and one end is (2, -3). If the abscissa of the other end is 10, what is the ordinate?
  A)
   3 or 9                    done clear
  B)
          -3 or-9 done clear
  C)
   3 or-9                   done clear
  D)
          -3 or 9 done clear
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• question_answer24)
  Which triangle is formed by the points A (2a, 4a), B (2a, 6a) and\[C(2a+\sqrt{3a},5a)\]?
  A)
   A right-angled triangle done clear
  B)
   An isosceles triangle done clear
  C)
   An equilateral triangle done clear
  D)
   An acute-angled triangle done clear
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• question_answer25)
  Find the perimeter of a triangle formed by (0, 0), (1, 0) and (0, 1).
  A)
   \[1\pm \sqrt{2}\]            done clear
  B)
          \[\sqrt{2}+1\] done clear
  C)
   3             done clear
  D)
          \[2+\sqrt{2}\] done clear
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• question_answer26)
  Let\[\Delta \text{ABC}\]be a triangle whose vertices are (0, 0), (a, 5) and (-5, 5) respectively. If the triangle is right-angled at A, find the value of 'a'.
  A)
   3                             done clear
  B)
          5 done clear
  C)
   2                             done clear
  D)
          6 done clear
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• question_answer27)
  The extremities of the diagonal of a parallelogram are the points (3, -4) and (-6, 5).Third vertex is the point (-2, 1). Find its fourth vertex.
  A)
   (1, 1)                     done clear
  B)
          (1, 0) done clear
  C)
   (0, 1)                     done clear
  D)
          (-1, 0) done clear
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• question_answer28)
  Find the third vertex of an equilateral triangle whose two vertices are (2, 4) and (2, 6).
  A)
   \[(\sqrt{3},5)\]                 done clear
  B)
          \[(2\sqrt{3},5)\] done clear
  C)
   \[(2+\sqrt{3},5)\]            done clear
  D)
          (2,5) done clear
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• question_answer29)
  A circle drawn with origin as the centre passes through \[\left( \frac{13}{2},0 \right)\] identify the point which does not lie in the interior of the circle.
  A)
   \[\left( \frac{-3}{4},1 \right)\]    done clear
  B)
          \[\left( 2,\frac{7}{3} \right)\] done clear
  C)
   \[\left( 5,\frac{1}{2} \right)\]     done clear
  D)
          \[\left( -6,\frac{5}{2} \right)\] done clear
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• question_answer30)
  Which of the following holds if the point \[p(x,y)\]is equidistant from \[\text{A(a}+\text{b},\text{b}-\text{a)}\]and \[\text{B(a}-\text{b},\text{a}+\text{b})\]?
  A)
   \[x=y\]                done clear
  B)
          \[ax=by\] done clear
  C)
   \[bx=ay\]           done clear
  D)
          \[xy=ab\] done clear
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• question_answer31)
  If P = (2, 5),\[Q=(x,-7)\]and PQ = 13, what is the value of 'x'?
  A)
   5                             done clear
  B)
          3 done clear
  C)
   -3                           done clear
  D)
          -5 done clear
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• question_answer32)
  What are the co-ordinates of the centroid of \[\Delta \text{ABC}\] with vertices A (-1, 0), B (5, -2) and C (8, 2).
  A)
   (12, 0)                  done clear
  B)
          (6, 0) done clear
  C)
   (0, 6)                     done clear
  D)
          (4, 0) done clear
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• question_answer33)
  Find the distance between the points\[(\sqrt{3}+1,\sqrt{2}-1)\]and\[(\sqrt{3}-1,\sqrt{2}+1)\].
  A)
   \[\sqrt{3}\]                        done clear
  B)
           \[2\sqrt{3}\] done clear
  C)
   \[\sqrt{2}\]                        done clear
  D)
          \[2\sqrt{2}\] done clear
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• question_answer34)
  Find the ratio in which the point P (m, 6) divides the join of A (-4,3) and B (2,8), and hence find the value of 'm'.
  A)
   \[\frac{1}{2}\]                   done clear
  B)
          \[\frac{3}{2}\] done clear
  C)
   \[\frac{-2}{5}\]                 done clear
  D)
          \[\frac{1}{3}\] done clear
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• question_answer35)
  The centre of a circle of radius 13 units is the point (3, 6). P (7, 9) is a point inside the circle.APB is a chord of the circle such that AP = PB. Find the length of AB.
  A)
   18 units               done clear
  B)
          12 units done clear
  C)
   24 units               done clear
  D)
          6 units done clear
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• question_answer36)
  The vertices of the triangle\[\Delta \text{ABC}\]are\[(\lambda ,2-2\lambda )\],\[(-\lambda ,+1,2\lambda )\]and\[(-4-\lambda ,6-2\lambda )\]. If its area is 70 sq. units, how many integral values does\[\lambda \]have?
  A)
   1                             done clear
  B)
          2 done clear
  C)
   4            done clear
  D)
          10 done clear
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• question_answer37)
  Which of the following is the quadrilateral formed by A (0, - 1), B (2, 1), C (0,3), D (- 2,1) taken in the same order?
  A)
   Rectangle           done clear
  B)
          Parallelogram done clear
  C)
   Square                 done clear
  D)
          Rhombus done clear
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• question_answer38)
  If two opposite vertices of a square are (1,-2) and (-5, 6), what are the other two vertices?
  A)
   (2, 5),(-6,-1)       done clear
  B)
          (-2,5), (6,1) done clear
  C)
   (2,-5),(6,-1)        done clear
  D)
          (2,-6),(5,-1) done clear
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• question_answer39)
  \[\Delta ABC\]is an isosceles triangle with B(1,3) and C (-2,7). Find the coordinates of A.
  A)
   \[\left( \frac{5}{6},6 \right)\]     done clear
  B)
          \[\left( 6,\frac{5}{6} \right)\] done clear
  C)
   \[\left( 7,\frac{1}{8} \right)\]     done clear
  D)
          \[\left( \frac{7}{8},1 \right)\] done clear
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• question_answer40)
  Vertices of a\[\Delta \text{ABC}\]are A (2,2), B (-4, -4) and C (5, -8). Find length of the median through C.
  A)
   \[\sqrt{65}\]                      done clear
  B)
          \[\sqrt{117}\] done clear
  C)
   \[\sqrt{85}\]                      done clear
  D)
          \[\sqrt{113}\] done clear
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• question_answer41)
  If the area of the triangle given in the figure is 20, what are the coordinates of the point C?
  A)
   \[\left( 0,\frac{40}{a} \right)\]   done clear
  B)
          \[({{a}^{2}}+{{b}^{2}},0)\] done clear
  C)
   \[\left( \frac{20}{b},0 \right)\]   done clear
  D)
          \[\left( \frac{40}{b},0 \right)\] done clear
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• question_answer42)
  In what ratio is the line segment joining the points (7,3) and (-4,5) divided by the Y-axis?
  A)
   2 : 3                       done clear
  B)
          4 : 7 done clear
  C)
   3 : 5                       done clear
  D)
          7 : 4 done clear
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• question_answer43)
  The mid-points of the sides AB and AC of a AABC are (3, 5) and (-3, -3) respectively. What is the length of the side BC?
  A)
   10                          done clear
  B)
          20   done clear
  C)
   15                          done clear
  D)
          30 done clear
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• question_answer44)
  In what ratio does the X-axis divide the line segment joining the points (3, -4) and (2,6)?
  A)
   2:3                         done clear
  B)
          3:2 done clear
  C)
   1:2                         done clear
  D)
          2:1 done clear
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• question_answer45)
  Find the point of trisection of the line joining the points (-2,-19) and (5, 4).
  A)
   (2,-3)                    done clear
  B)
          (1, 2) done clear
  C)
   \[\left( \frac{1}{3},-\frac{34}{3} \right)\]               done clear
  D)
          \[\left( \frac{8}{3},\frac{11}{3} \right)\] done clear
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• question_answer46)
  The mid points of three sides of a triangle are (5, -3), (-5, 3) and (6, 6). Find the vertices of the triangle.
  A)
   (16, 0), (-4, 12), (-6, -6) done clear
  B)
   (16, 8), (-4, 12), (6, -6) done clear
  C)
   (16, 0), (4, 12), (6, 6) done clear
  D)
   (8, 2), (-4, 12), (6, -6) done clear
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• question_answer47)
  If the co-ordinates of points A,B,C and D are (6, 3), (- 3, 5), (4, -2) and\[(x,3x)\]area of ADBC 1 respectively and if \[\frac{area\,of\,\Delta DBC}{area\,of\,\Delta ABC}=\frac{1}{4}\]' find the value of 'x'.
  A)
   \[\frac{8}{11}\] done clear
  B)
                          \[\frac{11}{8}\]   done clear
  C)
   \[\frac{7}{9}\]                                   done clear
  D)
          0 done clear
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• question_answer48)
  If the points (a, 0), (0, b) and (1,1) are collinear, which of the following is true?
  A)
   \[\frac{1}{a}+\frac{1}{b}=2\]                      done clear
  B)
   \[\frac{1}{a}-\frac{1}{b}=1\] done clear
  C)
   \[\frac{1}{a}-\frac{1}{b}=2\]       done clear
  D)
          \[\frac{1}{a}+\frac{1}{b}=1\] done clear
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• question_answer49)
  If A = (-3,4) and B = (2,1). what are the coordinates of the point C on AB produced such that AC = 2BC?
  A)
   (2, 4)                                     done clear
  B)
   (3, 7) done clear
  C)
   (7,-2)                    done clear
  D)
          (3, -2) done clear
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• question_answer50)
  Find the area of a quadrilateral ABCD with A(1,1), B (7, -3), C (12, 2) and D(7, 21) as its vertices.
  A)
   35 sq. units   done clear
  B)
          65 sq. units done clear
  C)
   85 sq. units   done clear
  D)
          132 sq. units done clear
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• question_answer51)
  In a parallelogram PQRS,P=(-1,-1), Q = (8, 0), R - (7, 5). What are the coordinates of 'S??
  A)
   (-1, 4)                   done clear
  B)
          (-2, 4) done clear
  C)
   (-2, 7/2)               done clear
  D)
          (-3/2, 4) done clear
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• question_answer52)
  What is the value of 'x' if (4, 3) and\[(x,5)\] are points on the circumference of a circle with centre O (2, 3)?
  A)
   4                             done clear
  B)
          2 done clear
  C)
   0                             done clear
  D)
          -2 done clear
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• question_answer53)
  Find the coordinates of the centroid of the triangle with vertices A (a, 0), B(0, b) and C (1,1).
  A)
   (0, a)                     done clear
  B)
          \[\left( \frac{a+1}{3},\frac{b+1}{3} \right)\] done clear
  C)
   (b, 0)                    done clear
  D)
          \[(\text{a}-\text{b},\text{a}+\text{b})\] done clear
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• question_answer54)
  Find the coordinates of the point that divides the line segment joining (-3, 5) and (4,-9) in the ratio 5 :2.
  A)
   (-2, -5)                                 done clear
  B)
   (-2, 5) done clear
  C)
   (2, 5)                     done clear
  D)
          (2, -5) done clear
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• question_answer55)
  What is the area of a triangle whose vertices are P (p, q + r), Q (q, r + p), and R(r, p + q)?
  A)
   16sq.units                          done clear
  B)
   12sq.units done clear
  C)
   19sq.units          done clear
  D)
          0 sq. units done clear
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