10th Class Mathematics Coordinate Geometry Question Bank

done Co-ordinatate Geometry Total Questions - 40

• question_answer1)
  PQOR is a rectangle whose vertices are Q (0, 7), O (0, 0) and R (- 5, 0). Find the length of its diagonal.
  A)
  \[\sqrt{84}\]     done clear
  B)
                                                         8            done clear
  C)
  12                                                                     done clear
  D)
  \[\sqrt{74}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  The point which lies on the perpendicular bisector of the line segmen joining the points P (- 3, - 5) and Q (3, 5) is
  A)
  (-3, 4)                                                                done clear
  B)
  (2, -5) done clear
  C)
  (0, 0)            done clear
  D)
  (-1, 4) done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer3)
  The points (- 5, 0), (0, 4) and (5, 1) are the vertices of a _______
  A)
  right triangle                                                       done clear
  B)
  isosceles triangle done clear
  C)
  equilateral triangle                                               done clear
  D)
  scalene triangle done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  The points (4, 5), (6, 7) and (8, 9) are ________
  A)
  collinear            done clear
  B)
  not collinear done clear
  C)
  the vertices of a right triangle    done clear
  D)
  vertices of an isosceles triangle done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  If a point (x, y) is equidistant from the points (p + q, q - p) and (p - q, p + q), then ________
  A)
  \[qx+yp=0\]                                          done clear
  B)
  \[qx=yp\]      done clear
  C)
   \[px=qy\]                                                         done clear
  D)
  \[px+qy=0\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer6)
  If M and N are the points whose coordinates are \[\left( \mathbf{a}{{\mathbf{p}}^{\mathbf{2}}},\text{ }\mathbf{2ap} \right)\] and \[\left( \frac{\mathbf{a}}{{{\mathbf{p}}^{\mathbf{2}}}}\mathbf{,}\frac{\mathbf{2a}}{\mathbf{p}} \right)\]  respectively and S is the point (a, 0), then \[\frac{\mathbf{1}}{\mathbf{SM}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{SN}}\] is equal to ____­­­­_____
  A)
  a                                                                      done clear
  B)
  ap           done clear
  C)
  \[\frac{1}{a}\]           done clear
  D)
  \[\frac{1}{ap}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer7)
  The coordinates of circumcentre of the triangle whose vertices are (3, 6),(4, -4) and (3, -5) are
  A)
  \[\left( \frac{-3}{2},\,\,0 \right)\]               done clear
  B)
  \[\left( \frac{-3}{2},\,\,\frac{1}{2} \right)\]     done clear
  C)
  \[\left( \frac{1}{2},\,\,-3 \right)\]               done clear
  D)
  \[\left( \frac{1}{3},\,\,\frac{3}{2} \right)\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  The ratio in which the line \[2x+3y-9=0\] the points (2, 3) and (4, 7) is _________
  A)
  3 : 1                                                                  done clear
  B)
  \[-\]5 : 4             done clear
  C)
  \[-\]1 : 5             done clear
  D)
  2 : 5 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  The area of a triangle, whose vertices are (a, a - 2), (a + 2, a + 2) and (a + 3, a), is _________
  A)
  1 sq unit                                                            done clear
  B)
  2 sq units     done clear
  C)
  3 sq units                                                           done clear
  D)
  4 sq units done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  If the points (p, 0), (0, q) and (1, 1) are collinear, then \[\frac{\mathbf{1}}{\mathbf{p}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{q}}\] equals to _______
  A)
  1 unit                done clear
  B)
  2 unit         done clear
  C)
  3 unit                done clear
  D)
  4 unit done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer11)
  The distance between the points\[(\cos \theta ,\sin \theta ,)\] and \[(\cos \theta ,-\sin \theta ,)\] is _______
  A)
  \[\sqrt{3}\]                     done clear
  B)
  \[\sqrt{2}\]           done clear
  C)
  2                      done clear
  D)
  1 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  If A \[\left( \frac{\mathbf{7}}{\mathbf{3}}\mathbf{,}\frac{\mathbf{m}}{\mathbf{5}} \right)\] is the midpoint of the line segment joining the points B (3, -2) and C (4, 6), then the value of m is _______
  A)
  4                                  done clear
  B)
  10           done clear
  C)
  \[-\]4                 done clear
  D)
  \[-\]8 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  If the point A (-3, m) divides the line segment joining the points B (-8, -5) and C (1, - 4) in the ratio a : b, then m equals to
  A)
  \[\frac{-5}{3}\]         done clear
  B)
  \[\frac{40}{3}\]           done clear
  C)
  \[\frac{-40}{9}\]             done clear
  D)
  \[\frac{30}{7}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  The ratio, in which the line 5x + 3y = - 9 divides the segment joining the points (2, 3) and (- 3, 4), is ________
  A)
  4 : 3                  done clear
  B)
  \[-\]4 : 3       done clear
  C)
  \[-\]14 : 5           done clear
  D)
  \[-\]14 : 3 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  If a point A (-1, 3) divides internally the line segment joining B (3, 4) and ( in ratio 2 : 3, then the coordinates of point C is ______
  A)
  (2,-3)                             done clear
  B)
  \[\left( 2,\frac{3}{2} \right)\]        done clear
  C)
  \[\left( -1,\frac{3}{2} \right)\]        done clear
  D)
  (-2, 3) done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  The points (6, 1), (8, 2), (9, 4) and (7, 3) are the vertices of a
  A)
  trapezium            done clear
  B)
  rectangle done clear
  C)
  square                                                   done clear
  D)
  rhombus done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  If the coordinates of mid-point of the sides of a triangle are (21, 7), (- 5, 8, 5) and (10, 8.5), then which among the following is not a vertex of this triangle?
  A)
  (\[-\]16, 10)                                            done clear
  B)
  (7, 6)          done clear
  C)
  (36, 7)                                                               done clear
  D)
  (6, 7) done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  The third vertex of a triangle, if two of its vertices are (- 5, 2) and (1, - 3) and the centroid is at (- 2, 3), is
  A)
  (- 2, 5)                                                               done clear
  B)
   (- 2, 10)       done clear
  C)
  (0, 5)                                                                 done clear
  D)
  (10, - 2) done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer19)
  The vertices of a \[\Delta \]PQR are P (1, 2), Q (- 3, 2) and R (5 - 6). Which among the following is a true statement for this triangle PQR?
  A)
  Circumcentre of \[\Delta \]PQR is (- 1, - 4) done clear
  B)
  Circumradius of\[\Delta \]PQR is 740 unit done clear
  C)
  The point where perpendicular bisectors of PQ and PR intersects, is the circumcentre of the triangle PQR. done clear
  D)
  All the above done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer20)
  Find the orthecentre of the triangle ABC having its vertices as A (- 2, - 3), B (2, 1) and C (5, - 2).
  A)
  (\[-\]3, 5)                                                            done clear
  B)
  (\[-\]4, 6)        done clear
  C)
  (2, 1)         done clear
  D)
  (0, 0) done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  The equation of a line whose inclination is \[60{}^\circ \] an of 5 units on x-axis, is
  A)
  \[\sqrt{3}x-y=\sqrt{3}\]                                                  done clear
  B)
  \[\sqrt{3}x-y=5\sqrt{3}\] done clear
  C)
  \[x-\sqrt{3}y=\sqrt{3}\]                                                  done clear
  D)
  \[x-\sqrt{3}y=5\sqrt{3}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer22)
  The area of a triangle formed by the line \[\mathbf{4x}-\mathbf{3y}+\mathbf{12}=\mathbf{0}\] with the coordinate axes is __________
  A)
  3 sq unit                                                            done clear
  B)
  4 sq unit      done clear
  C)
  5 sq unit                                                            done clear
  D)
  6 sq unit done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  The equation of a line which is parallel to the line \[\mathbf{3x}-\mathbf{5y}+\mathbf{8}=\mathbf{0}\] and making an intercept - 3 on x-axis is
  A)
  \[5y-3x=9\]      done clear
  B)
  \[5y+3x=9\] done clear
  C)
  \[3x+5y=9\]                                                      done clear
  D)
  \[3x-5y=9\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  Which among the following can be the vertices of an equilateral triangle?
  A)
  (2, 3), (5, 4), (7, 8) done clear
  B)
  (3, - 6), (5,-9), (6, - 12) done clear
  C)
  (3,-3), (-3, 3), \[(-3\sqrt{3},-3\sqrt{3)}\] done clear
  D)
  All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer25)
  If the vertices of a triangle have integral coordinates, then the triangle cannot be
  A)
  an equilateral triangle       done clear
  B)
  a right triangle done clear
  C)
  an isosceles triangle            done clear
  D)
  All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer26)
  If three vertices (in order) of a parallelogram are (p + q, p - q), (2p + q, 2p q) and (p - q, p + q), then its fourth vertex is  _________
  A)
  \[\left( q,\,\,-q \right)\]                                                                  done clear
  B)
  \[\left( 2q,\,\,-2q \right)\]     done clear
  C)
  \[\left( -\,q,\,\,q \right)\]      done clear
  D)
  \[\left( p,\,-p \right)\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  The equation of median drawn from the vertex P to the side QR of a \[\Delta \]PQR, whose vertices are P (2, 3), Q (- 3, - 5) and R (6, 2), is _______.
  A)
  \[9x-y=18\]                                                                    done clear
  B)
  \[9x-y=15\] done clear
  C)
  \[3x-8y=18\]                                                      done clear
  D)
  \[3x+8y=15\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer28)
  A line \[\mathbf{6x}+\mathbf{5y}=\mathbf{30}\] intersects the coordinate axes. Find the length of the smallest side of the triangle so formed by the axis.
  A)
  3 units                                                               done clear
  B)
  4 units done clear
  C)
  5 units           done clear
  D)
  6 units done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  The line segment joining the points (3, - 2) and (4, - 6) is divided by the line \[\mathbf{2x}+\mathbf{3y}-\mathbf{11}=\mathbf{0}\] in the ratio m: n externally at point (a, b). Which among the following is true for the given information?
  A)
  m = 11                                                             done clear
  B)
  n = 21 done clear
  C)
  \[a-b=\frac{89}{10}\]                                                                 done clear
  D)
   All the above done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  If the mid-points of sides of a \[\Delta \]ABC are P (2, 5), Q (- 3, 8) and R (6, 12), then its vertices are ________
  A)
  (13, 10), (\[-\]9, 2), (2, 14) done clear
  B)
  (12, 9), (\[-\]8, 1), (1, 15) done clear
  C)
  (11, 9), (\[-\]7, 1), (1, 15) done clear
  D)
  (\[-\]12, 8), (\[-\]7, 2), (\[-\]2, 15) done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  The three medians of a \[\Delta \]PQR intersect at a point S. If the medians are PM, QN & RT and the area of \[\Delta \]PQR is 90\[c{{m}^{2}}\], then the area of the quadrilateral MSRN is ________
  A)
  45 \[c{{m}^{2}}\]                                                                    done clear
  B)
  30 \[c{{m}^{2}}\] done clear
  C)
  15 \[c{{m}^{2}}\]                                                                    done clear
  D)
  60 \[c{{m}^{2}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  The length of the side of a at the of the angle of Pythagorean triangle of     8 cm, 15 cm 17 cm the hypotenuse is ________
  A)
  \[5\frac{5}{23}cm\]                 done clear
  B)
  \[6\frac{4}{23}cm\] done clear
  C)
   \[7\frac{3}{23}cm\]                                                       done clear
  D)
   \[4\frac{2}{23}cm\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  The length of the diagonal of a square, which can be inscribed in a right triangle of sides 5 cm, 12 cm and 13 cm, is ______
  A)
  \[\frac{30\sqrt{2}}{17}cm\]                                            done clear
  B)
  \[\frac{60\sqrt{2}}{17}cm\] done clear
  C)
  15 cm                                                               done clear
  D)
  10\[\sqrt{2}\] cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  The equation of a line, which passes through (3, 4) and the product of whose intercepts on the coordinate axes is 48, is _________
  A)
  \[6x+9y=48\]                                        done clear
  B)
   \[8x+9y=48\] done clear
  C)
  \[4x+3y=24\]      done clear
  D)
  \[3x+4y=24\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer35)
  If the equations of three concurrent lines are \[\mathbf{px}+\mathbf{6y}-\mathbf{8}=\mathbf{0},\] \[\mathbf{qx}+\mathbf{5y}-\mathbf{8}=\mathbf{0}\] and \[\mathbf{rx}+\mathbf{4y}-\mathbf{8}=\mathbf{0},\] then the value of p + r is __________
  A)
  q                                                                      done clear
  B)
  2q done clear
  C)
  3q                                                                     done clear
  D)
  4q done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  The point (p, q) divides the line formed by joining the points (p + q, p + q) and (p - q, q - p) in the ratio _______
  A)
  p : q internally                                                    done clear
  B)
  q : p externally done clear
  C)
   2 : 1                                                                 done clear
  D)
   1 : 1 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  The radius of the circle which passes through the origin (0, 6) and (6, 0) is
  A)
  12cm                                                                done clear
  B)
   6 cm done clear
  C)
  3\[\sqrt{2}\]cm            done clear
  D)
  4\[\sqrt{2}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer38)
  Area of the region formed by the lines \[3|x|+\,2|y|\,=6\] is
  A)
  8\[c{{m}^{2}}\]                                                           done clear
  B)
  10\[c{{m}^{2}}\] done clear
  C)
  12\[c{{m}^{2}}\]         done clear
  D)
  14\[c{{m}^{2}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  The orthecentre of the triangle formed by the lines \[\mathbf{5x}-\mathbf{8y}=\mathbf{10},\] \[\mathbf{16x}+\mathbf{10y}=\mathbf{13}\] and y-axis, is _____      
  A)
  \[\left( \frac{102}{89},\frac{-95}{178} \right)\]    done clear
  B)
  \[\left( \frac{51}{89},\frac{89}{95} \right)\]    done clear
  C)
  \[\left( \frac{102}{89},\frac{95}{178} \right)\]       done clear
  D)
  \[\left( \frac{51}{89},\frac{-95}{89} \right)\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer40)
  The line which is perpendicular to \[\mathbf{5x}+\mathbf{2y}-\mathbf{3}=\mathbf{0}\] is _________
  A)
  \[2x-5y+8=0\]               done clear
  B)
   \[3x-5y=9\] done clear
  C)
  \[4x-3y=7\]                                                        done clear
  D)
  \[5x-2y=3\] done clear
  E)
  None of these done clear
  View Solution play_arrow