JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank

done System of co-ordinates, Distance between two points, Section formulae Total Questions - 44

• question_answer1)
  The coordinates of a point are (0, 1) and the ordinate of another point is - 3. If the distance between the two points is 5, then the abscissa of another point is  
  A)
  3 done clear
  B)
  - 3 done clear
  C)
  \[\pm 3\] done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer2)
  One of the vertices of a square is origin and adjacent sides of the square are coincident with positive axes. If side is 5 then which will not be its one of the vertex
  A)
  (0, 5) done clear
  B)
  (5, 0) done clear
  C)
  (- 5, - 5) done clear
  D)
  (0, 0) done clear
  View Solution play_arrow

• question_answer3)
  The common property of points lying on x-axis, is      [MP PET 1988]
  A)
  \[x=0\] done clear
  B)
  \[y=0\] done clear
  C)
  \[a=0,\,y=0\] done clear
  D)
  \[y=0,b=0\] done clear
  View Solution play_arrow

• question_answer4)
  If the distance between the points \[(a,2)\]and \[(3,4)\]be 8, then \[a=\]    [MNR 1978]
  A)
  \[2+3\sqrt{15}\] done clear
  B)
  \[2-3\sqrt{15}\] done clear
  C)
  \[2\pm 3\sqrt{15}\] done clear
  D)
  \[3\pm 2\sqrt{15}\] done clear
  View Solution play_arrow

• question_answer5)
  The point whose abscissa is equal to its ordinate and which is equidistant from the points (1,0) and (0,3) is
  A)
  (1, 1) done clear
  B)
  (2, 2) done clear
  C)
  (3, 3) done clear
  D)
  (4, 4) done clear
  View Solution play_arrow

• question_answer6)
  If the points \[A(6,-1),\ B\text{ }(1,\,3)\] and \[C(x,\,8)\]be such that \[AB=BC,\]then  \[x=\]
  A)
  - 3, 5 done clear
  B)
  3, - 5 done clear
  C)
  - 3, - 5 done clear
  D)
  3, 5 done clear
  View Solution play_arrow

• question_answer7)
  The distance between the points \[(am_{1}^{2},\,2a{{m}_{1}})\] and \[(am_{2}^{2},\,2a{{m}_{2}})\] is
  A)
  \[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\] done clear
  B)
  \[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}+4}\] done clear
  C)
  \[a({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\] done clear
  D)
  \[({{m}_{1}}-{{m}_{2}})\sqrt{{{({{m}_{1}}+{{m}_{2}})}^{2}}-4}\] done clear
  View Solution play_arrow

• question_answer8)
  If the point (x, y) be equidistant from the points \[(a+b,\,b-a)\]and \[(a-b,\,a+b),\]then [MP PET 1983, 94]
  A)
  \[ax+by=0\] done clear
  B)
  \[ax-by=0\] done clear
  C)
  \[bx+ay=0\] done clear
  D)
  \[bx-ay=0\] done clear
  View Solution play_arrow

• question_answer9)
  If the points (0, 0), \[(2,\,2\sqrt{3})\] and (a, b) be the vertices of an equilateral triangle, then \[(a,\,b)=\]
  A)
  (0, - 4) done clear
  B)
  (0, 4) done clear
  C)
  (4, 0) done clear
  D)
  (- 4, 0) done clear
  View Solution play_arrow

• question_answer10)
  The distance between the points \[(a\cos \alpha ,\,a\sin \alpha )\] and \[(a\cos \beta ,a\sin \beta )\]is 
  A)
  \[a\cos \frac{\alpha -\beta }{2}\] done clear
  B)
  \[2a\cos \frac{\alpha -\beta }{2}\] done clear
  C)
  \[a\sin \frac{\alpha -\beta }{2}\] done clear
  D)
  \[2a\sin \frac{\alpha -\beta }{2}\] done clear
  View Solution play_arrow

• question_answer11)
  A point equidistant from the points (2, 0) and (0, 2) is
  A)
  (1, 4) done clear
  B)
  (2, 1) done clear
  C)
  (1, 2) done clear
  D)
  (2, 2) done clear
  View Solution play_arrow

• question_answer12)
  The point on y-axis equidistant from the points (3, 2) and  (-1, 3) is 
  A)
  (0, -3) done clear
  B)
  (0, -3/2) done clear
  C)
  (0, 3/2) done clear
  D)
  (0, 3) done clear
  View Solution play_arrow

• question_answer13)
  If a vertex of an equilateral triangle is on origin and second vertex is (4, 0), then its third vertex is
  A)
  \[(2,\,\pm \sqrt{3})\] done clear
  B)
  \[(3,\,\pm \sqrt{2})\] done clear
  C)
  \[(2,\,\pm 2\sqrt{3})\] done clear
  D)
  \[(3,\,\pm 2\sqrt{2})\] done clear
  View Solution play_arrow

• question_answer14)
  If the coordinates of vertices of \[\Delta OAB\] are (0,0) \[(\cos \alpha ,\,\sin \alpha )\] and \[(-\sin \alpha ,\,\cos \alpha )\] respectively, then \[O{{A}^{2}}+O{{B}^{2}}=\] 
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer15)
  The length of altitude through A of the triangle ABC, where \[A\equiv (-3,\,0);\,B\equiv (4,\,-1);\,C\equiv (5,\,2),\] is  [Karnataka CET 2001]
  A)
  \[\frac{2}{\sqrt{10}}\] done clear
  B)
  \[\frac{4}{\sqrt{10}}\] done clear
  C)
  \[\frac{11}{\sqrt{10}}\] done clear
  D)
  \[\frac{22}{\sqrt{10}}\] done clear
  View Solution play_arrow

• question_answer16)
  The distance of the point \[(b\cos \theta ,\,b\sin \theta )\]from origin is   [MP PET 1984]
  A)
  \[b\cot \theta \] done clear
  B)
  \[b\] done clear
  C)
  \[b\tan \theta \] done clear
  D)
  \[b\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer17)
  The distance of the middle point of the line joining the points \[(a\sin \theta ,0)\]and \[(0,a\cos \theta )\]from the origin is    [MP PET 1999]
  A)
  \[\frac{a}{2}\] done clear
  B)
  \[\frac{1}{2}a(\sin \theta +\cos \theta )\] done clear
  C)
  \[a(\sin \theta +\cos \theta )\] done clear
  D)
  \[a\] done clear
  View Solution play_arrow

• question_answer18)
  If the points (1,1), (-1, -1) and \[(-\sqrt{3},k)\]are vertices of an equilateral triangle then the value of k will be
  A)
  1 done clear
  B)
  -1 done clear
  C)
  \[\sqrt{3}\] done clear
  D)
  \[-\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer19)
  The points P is equidistant from A(1,3), B (-3,5) and C(5,-1). Then PA =    [EAMCET 2003]
  A)
  5 done clear
  B)
  \[5\sqrt{5}\] done clear
  C)
  25 done clear
  D)
  \[5\sqrt{10}\] done clear
  View Solution play_arrow

• question_answer20)
  The distance between the points (7, 5) and (3, 2) is equal to   [Pb. CET 2002]
  A)
  2 units done clear
  B)
  3 units done clear
  C)
  4 units done clear
  D)
  5 units done clear
  View Solution play_arrow

• question_answer21)
  If the point dividing internally the line segment joining the points (a, b) and (5, 7) in the ratio 2 : 1 be (4, 6), then  
  A)
  \[a=1,\,b=2\] done clear
  B)
  \[a=2,\,b=-4\] done clear
  C)
  \[a=2,\,b=4\] done clear
  D)
  \[a=-2,\,b=4\] done clear
  View Solution play_arrow

• question_answer22)
  If the middle point of the line segment joining the points (5, a) and (b,7) be (3,5), then (a, b) =
  A)
  (3, 1) done clear
  B)
  (1, 3) done clear
  C)
  (-2,-2) done clear
  D)
  (-3, -1) done clear
  View Solution play_arrow

• question_answer23)
  The ratio in which x-axis divides the join of the points (2, -3) and (5, 6) is 
  A)
  2 : 1 done clear
  B)
  1: 2 done clear
  C)
  2 : -1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  The point which divides externally the line joining the points \[(a+b,\,a-b)\] and \[(a-b,a+b)\] in the ratio \[a:b\], is
  A)
  \[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\] done clear
  B)
  \[\left( \frac{{{a}^{2}}-2ab-{{b}^{2}}}{a-b},\frac{{{a}^{2}}-{{b}^{2}}}{a-b} \right)\] done clear
  C)
  \[\left( \frac{{{a}^{2}}-2ab+{{b}^{2}}}{a-b},\frac{{{a}^{2}}+{{b}^{2}}}{a-b} \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  The coordinates of the points A, B, C are \[({{x}_{1}},{{y}_{1}})\], \[({{x}_{2}},{{y}_{2}})\], \[({{x}_{3}},\,{{y}_{3}})\] and D divides the line AB in the ratio l : k. If P divides the line DC in the ratio m : k + l, then the coordinates of P are
  A)
  \[\left( \frac{k{{x}_{1}}+l{{x}_{2}}+m{{x}_{3}}}{k+l+m},\,\frac{k{{y}_{1}}+l{{y}_{2}}+m{{y}_{3}}}{k+l+m} \right)\] done clear
  B)
  \[\left( \frac{l{{x}_{1}}+m{{x}_{2}}+k{{x}_{3}}}{l+m+k},\,\frac{l{{y}_{1}}+m{{y}_{2}}+k{{y}_{3}}}{l+m+k} \right)\] done clear
  C)
  \[\left( \frac{m{{x}_{1}}+k{{x}_{2}}+l{{x}_{3}}}{m+k+l},\,\frac{m{{y}_{1}}+k{{y}_{2}}+l{{y}_{3}}}{m+k+l} \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  The points which trisect the line segment joining the points (0, 0) and (9, 12) are    [RPET 1986]
  A)
  (3, 4), (6, 8) done clear
  B)
  (4, 3), (6, 8) done clear
  C)
  (4, 3), (8, 6) done clear
  D)
  (3, 4), (8, 6) done clear
  View Solution play_arrow

• question_answer27)
  The line \[x+y=4\] divides the line joining the points (-1, 1) and (5, 7) in the ratio       [IIT 1965; UPSEAT 1999]
  A)
  2 : 1 done clear
  B)
  1 : 2 done clear
  C)
  1 : 2 externally  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer28)
  If the point (x, - 1), (3, y), (- 2, 3) and (- 3, - 2) be the vertices of a parallelogram, then
  A)
  \[x=2,\,y=4\] done clear
  B)
  \[x=1,\,y=2\] done clear
  C)
  \[x=4,\,y=2\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  The mid-points of sides of a triangle are (2, 1), (-1, -3) and (4,5). Then the coordinates of its vertices are
  A)
  \[(7,\,9),\,(-3,\,-7),\,(1,\,1)\] done clear
  B)
  \[(-3,\,-7),\,(1,\,1),\,(2,\,3)\] done clear
  C)
  \[(1,\,1),\,(2,\,3),\,(-5,\,8),\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  Point \[\left( \frac{1}{2},\,\frac{-13}{4} \right)\]divides the line joining the points \[(3,-5)\]and \[(-7,2)\] in the ratio of 
  A)
  1 : 3 internally done clear
  B)
  3 : 1internally done clear
  C)
  1 : 3 externally done clear
  D)
  3 : 1externally done clear
  View Solution play_arrow

• question_answer31)
  The coordinates of the join of trisection of the points (­-2, 3), (3, -1) nearer to (-2, 3), is
  A)
  \[\left( -\frac{1}{3},\,\frac{5}{3} \right)\] done clear
  B)
  \[\left( \frac{4}{3},\frac{1}{3} \right)\] done clear
  C)
  \[\left( -\frac{3}{4},\,2 \right)\] done clear
  D)
  \[\left( \frac{1}{3},\,\frac{5}{3} \right)\] done clear
  View Solution play_arrow

• question_answer32)
  If the vertices of a triangle are \[A(1,4),\,B(3,0)\]and \[C(2,1),\]then the length of the median passing through C is  [RPET 1995]
  A)
  1 done clear
  B)
  2 done clear
  C)
  \[\sqrt{2}\] done clear
  D)
  \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer33)
  Three vertices of a parallelogram taken in order are \[(-1,\,-6)\], \[(2,\,-5)\] and \[(7,\,2)\]. The fourth vertex is  [Kerala (Engg.) 2002]
  A)
  (1, 4) done clear
  B)
  (4, 1) done clear
  C)
  (1, 1) done clear
  D)
  (4, 4) done clear
  View Solution play_arrow

• question_answer34)
  P and Q are points on the line joining A (­-2, 5) and B (3, 1) such that AP = PQ = QB. Then the mid-point of PQ is  
  A)
  \[\left( \frac{1}{2},\,3 \right)\] done clear
  B)
  \[\left( -\frac{1}{2},\,4 \right)\] done clear
  C)
  \[(2,\,3)\] done clear
  D)
  \[(1,\,4)\] done clear
  View Solution play_arrow

• question_answer35)
  The points of trisection of the line segment joining the points (3, -2) and (-3, -4) are
  A)
  \[\left( \frac{3}{2},-\frac{5}{2} \right)\,,\left( -\frac{3}{2},-\frac{13}{4} \right)\] done clear
  B)
  \[\left( -\frac{3}{2},\frac{5}{2} \right)\,,\left( \frac{3}{2},\frac{13}{4} \right)\] done clear
  C)
  \[\left( 1,-\frac{8}{3} \right)\,,\left( -1,-\frac{10}{3} \right)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  The coordinates of the point dividing internally the lines joining the points (4, -2) and (8, 6) in the ratio 7 : 5 will be [AMU 1979; MP PET 1984]
  A)
  \[(16,\,18)\] done clear
  B)
  \[(18,\,16)\] done clear
  C)
  \[\left( \frac{19}{3},\,\frac{8}{3} \right)\] done clear
  D)
  \[\left( \frac{8}{3},\frac{19}{3} \right)\] done clear
  View Solution play_arrow

• question_answer37)
  In what ratio does the y-axis divide the join of \[(-3,\,-4)\]and \[(1,-2)\]   [RPET 1995]
  A)
  1 : 3 done clear
  B)
  2 : 3 done clear
  C)
  3 : 1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer38)
  If the three vertices of a rectangle taken in order are the points (2, -2), (8, 4) and (5, 7). The coordinates of the fourth vertex is   [CEE 1993]
  A)
  (1, 1) done clear
  B)
  (1, -1) done clear
  C)
  (-1, 1) done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  The line joining points (2, -3) and (-5,6) is divided by y-axis in the ratio   [MP PET 1999]
  A)
  2 : 5 done clear
  B)
  2 : 3 done clear
  C)
  3 : 5 done clear
  D)
  1 : 2 done clear
  View Solution play_arrow

• question_answer40)
  If P (1,2), Q(4,6) R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then  [IIT 1998]
  A)
  \[a=2,\,b=4\] done clear
  B)
  \[a=3,\,b=4\] done clear
  C)
  \[a=2,\,b=3\] done clear
  D)
  \[a=3,\,b=5\] done clear
  View Solution play_arrow

• question_answer41)
  The extremities of a diagonal of a parallelogram are the points \[(3,-4)\]and \[(-6,5)\]. If third vertex is \[(-2,1)\], then fourth vertex is [RPET 1987]
  A)
  \[(1,0)\] done clear
  B)
  \[(-1,0)\] done clear
  C)
  \[(1,\text{ }1)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  (0, -1) and (0, 3) are two opposite vertices of a square. The other two vertices are   [Karnataka CET 2005]
  A)
  (0, 1), (0, -3) done clear
  B)
  (3, -1) (0, 0) done clear
  C)
  (2, 1), (-2, 1) done clear
  D)
  (2, 2), (1, 1) done clear
  View Solution play_arrow

• question_answer43)
  If \[A(3,\,5),B(-5,\,-4),C(7,\,10)\] are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are [Kerala (Engg.) 2005]
  A)
  (10, 19) done clear
  B)
  (15, 10) done clear
  C)
  (19, 10) done clear
  D)
  (19, 15) done clear
  E)
  (e) (15, 19) done clear
  View Solution play_arrow

• question_answer44)
  If  the point (a, a) are placed in between the lines \[|x+y|=4\], then  [AMU 2005] 
  A)
  | a| = 2 done clear
  B)
   \[|a|\,=3\] done clear
  C)
  | a| < 2 done clear
  D)
  | a| < 3 done clear
  View Solution play_arrow