10th Class Mathematics Coordinate Geometry Question Bank

done MCQs - Coordinate Geometry Total Questions - 50

• question_answer1)
  In the given figure, O is the intersecting point of OA and OC and OABC is a square of side 4 units, then the position of A, B and C is
  A)
  (4,0)(4,4)(0,4) done clear
  B)
  (4,0)(0,4)(4,4) done clear
  C)
  (0,4)(4,4)(4,0) done clear
  D)
  None of the above done clear
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• question_answer2)
   

  In the given figure, the ordinates of the points P, Q, R and S is

   
  A)
  2,-2,-5,5 done clear
  B)
  3,4,-3,-1 done clear
  C)
  3,4,-5,5 done clear
  D)
  2,4,-5,-1 done clear
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• question_answer3)

  The coordinates of the point P as shown in the diagram will be

   
  A)
  (2, -3) done clear
  B)
  (-3, 2) done clear
  C)
  (2, 3) done clear
  D)
  (3, 2) done clear
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• question_answer4)
  The coordinate of the vertices of a rectangle whose length and breadth are 6 and 4 units, respectively. Its one vertex is at the origin. The longer side is on the X-axis and one of the vertices lies in second quadrant is
  A)
  (0,0)(6,4)(6,0)(0,4) done clear
  B)
  (0,0)(0,4)(6,0)(6,4) done clear
  C)
  (0,0)(6,4)(-6,0)(6,4) done clear
  D)
  (0,0)(0,4)(-6,4)(-6,0) done clear
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• question_answer5)
  The point \[P\left( -4,\,2 \right)\]lies on the line segment joining the points \[A\left( -4,\,6 \right)\]and\[B\left( -4,\,-6 \right)\].
  A)
  True done clear
  B)
  False done clear
  C)
  Can't say done clear
  D)
  Partially True/False done clear
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• question_answer6)
  The distance of the point P(2, 3) from the X-axis is
  A)
  2 units done clear
  B)
  3 units done clear
  C)
  1 units done clear
  D)
  5 units done clear
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• question_answer7)
  The distance between the points \[P\left( -6,\,7 \right)\] and \[Q\left( -1,\,-5 \right)\]is
  A)
  -6 units done clear
  B)
  13 units done clear
  C)
  1 units done clear
  D)
  5 units done clear
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• question_answer8)
  The distance between the points \[\left( a\,\cos \theta +b\,\sin \theta ,\,0 \right)\]and\[\left( 0,\,a\,\sin \theta -b\,\cos \theta  \right)\]is
  A)
  \[{{a}^{2}}+{{b}^{2}}\] done clear
  B)
  \[{{a}^{2}}-{{b}^{2}}\] done clear
  C)
  \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] done clear
  D)
  \[\sqrt{{{a}^{2}}-{{b}^{2}}}\] done clear
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• question_answer9)
  The value of y, if the distance between the points (2, y) and (-4, 3) is 10 is
  A)
  6 done clear
  B)
  -11 done clear
  C)
  5 done clear
  D)
  11 done clear
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• question_answer10)
  Point P(0, 2) is the point of intersection of Y-axis and perpendicular bisector of line segment joining the points A (-1, 1) and 5(3, 3).
  A)
  True done clear
  B)
  False done clear
  C)
  Can't say done clear
  D)
  Partially True/False done clear
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• question_answer11)
  If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
  A)
  4 done clear
  B)
  -4 done clear
  C)
  Both [a] and [b] done clear
  D)
  0 done clear
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• question_answer12)
  A circle has its centre at the origin and a point P (5, 0) lies on it. The point \[Q\left( 6,\,8 \right)\]lies outside the circle.
  A)
  True done clear
  B)
  False done clear
  C)
  Can't say done clear
  D)
  Partially True/False done clear
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• question_answer13)
  The radius of the circles whose centre is at (0, 0) and which passes through the points (- 6, 8) is ............ .
  A)
  10 units done clear
  B)
  11 units done clear
  C)
  9 units done clear
  D)
  8 units done clear
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• question_answer14)
  Is the points (1, - 1), (5, 2) and (9, 5) are collinear?
  A)
  Yes done clear
  B)
  No done clear
  C)
  Can't find done clear
  D)
  None of the above done clear
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• question_answer15)
  If the point P(2,1) lies on the line segment joining points A(4, 2) and 5(8, 4), then ..........
  A)
  \[AP=\frac{1}{3}AB\] done clear
  B)
  \[AP=PB\] done clear
  C)
  \[PB=\frac{1}{3}AB\] done clear
  D)
  \[AP=\frac{1}{2}AB\] done clear
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• question_answer16)
  If the point P (x, y) is equidistant from the points A(5, 1) and 5(1, 5), then
  A)
  y=3x done clear
  B)
  x=y done clear
  C)
  x=-8y done clear
  D)
  -8x=y done clear
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• question_answer17)
  A point on X-axis which is equidistant from the points (1, 3) and (-1, 2).
  A)
  (5/2,0) done clear
  B)
  (5,0) done clear
  C)
  (4, 0) done clear
  D)
  (5/4,0) done clear
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• question_answer18)
  The point on X-axis, which is equidistant from the point (7, 6) and (-3, 4) is
  A)
  (0, 3) done clear
  B)
  (4, 3) done clear
  C)
  (3, 0) done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer19)
   

  The coordinates of the point which is equidistant from the three vertices of the \[\Delta AOB\]  as shown in the figure is a

  A)
  (x, y) done clear
  B)
  (y, x) done clear
  C)
  \[\left( \frac{x}{2},\,\frac{y}{2} \right)\] done clear
  D)
  \[\left( \frac{y}{2},\,\frac{x}{2} \right)\] done clear
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• question_answer20)
  The coordinate of a point on Y-axis which is equidistant from the point \[A\left( 6,\,5 \right)\]and\[B\left( -4,\,3 \right)\], will be
  A)
  (0, 9) done clear
  B)
  (0, -9) done clear
  C)
  (0, 5) done clear
  D)
  (0, 3) done clear
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• question_answer21)
  The radius of the circle whose end points of diameter are (24, 1) and (2, 23) is
  A)
  \[22\sqrt{2}\]units done clear
  B)
  \[23\sqrt{2}\]units done clear
  C)
  \[11\sqrt{2}\] units done clear
  D)
  None of these done clear
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• question_answer22)
  If the points A (4, 3) and B (x, S) are on the circle with centre O (2, 3), then the value of x is
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
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• question_answer23)
  The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
  A)
  5 units done clear
  B)
  12 units done clear
  C)
  11 units done clear
  D)
  \[\left( 7+\sqrt{5} \right)\]units done clear
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• question_answer24)
  If three points (0, 0), \[\left( 3,\,\sqrt{3} \right)\]and \[\left( 3,\,\lambda  \right)\]form an equilateral triangle, then \[\lambda \], equals
  A)
  2 done clear
  B)
  -3 done clear
  C)
  -4 done clear
  D)
  None of these done clear
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• question_answer25)
  If AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B (5, 0), then the length of its diagonal is   
  A)
  5 units done clear
  B)
  3 units done clear
  C)
  \[\sqrt{34}\]units done clear
  D)
  A units done clear
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• question_answer26)
  The points (3, 2), (-2, - 3) and (2, 3) form a triangle name the type of triangle formed.
  A)
  equilateral done clear
  B)
  isosceles done clear
  C)
  right angle done clear
  D)
  None of these done clear
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• question_answer27)
  (5, - 2), (6, 4) and (7, - 2) are the vertices of an ......... triangle.
  A)
  equilateral done clear
  B)
  right angle done clear
  C)
  isosceles done clear
  D)
  None of these done clear
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• question_answer28)
  The points (- 4, 0), (4, 0) and (0, 3) are the vertices of a
  A)
  right angled triangle done clear
  B)
  isosceles triangle done clear
  C)
  equilateral triangle done clear
  D)
  scalene triangle done clear
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• question_answer29)
  The points (2, 3), (3, 4), (5, 6) and (4, 5) are the vertices of a
  A)
  Parallelogram done clear
  B)
  Triangle done clear
  C)
  Square done clear
  D)
  None of these done clear
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• question_answer30)
  The coordinates of the point which divides the line segment joining the points (4, - 3) and (9, 7) internally in the ratio 3: 2 is
  A)
  (7, 3) done clear
  B)
  (3, 7) done clear
  C)
  (35, 15) done clear
  D)
  (27, 21) done clear
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• question_answer31)
  The point which divides the line segment joining the points (7, - 6) and (3, 4) in ratio 1 : 2 internally lies in the
  A)
  I quadrant done clear
  B)
  II quadrant done clear
  C)
  III quadrant done clear
  D)
  IV quadrant done clear
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• question_answer32)
  If \[P\left( 9a-2,\,-b \right)\]divides line segment joining \[A\left( 3a+1,\,-3 \right)\] and \[B\left( 8a,\,5 \right)\]in the ratio 3 : 1, then the values of a and b is
  A)
  \[a=-1,\,b=3\] done clear
  B)
  \[a=-1,\,b=-3\] done clear
  C)
  \[a=0,\,b=0\] done clear
  D)
  \[a=1,\,b=-3\] done clear
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• question_answer33)
  The point (-4, 6) divides the line segment joining the points \[A\left( -6,\text{ }10 \right)\]and B (3,-8). The ratio is
  A)
  1 : 2 done clear
  B)
  7 : 2 done clear
  C)
  2 : 7 done clear
  D)
  4 : 1 done clear
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• question_answer34)
  If \[P\left( \frac{a}{3},4 \right)\]is the mid-point of the line segment joining the points \[Q\left( -6,\,5 \right)\]and\[R\left( -2,\,3 \right)\], then the value of a is
  A)
  -4 done clear
  B)
  -12 done clear
  C)
  12 done clear
  D)
  -6 done clear
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• question_answer35)
  The fourth vertex D of a parallelogram ABCD whose three vertices are A (- 2, 3), 5(6, 7) and C(8, 3) is
  A)
  (0, 1) done clear
  B)
  (0, -1) done clear
  C)
  (-1, 0) done clear
  D)
  (1, 0) done clear
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• question_answer36)
  If \[x-2y+k=0\]is a median of the triangle whose vertices are at points A (- 1, 3), B (0, 4) and C (- 5, 2), then the value of k is
  A)
  2 done clear
  B)
  4 done clear
  C)
  6 done clear
  D)
  8 done clear
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• question_answer37)
  The perpendicular bisector of the line segment joining the points \[A\left( -2,\,-5 \right)\] and \[B\left( 4,\,6 \right)\]cuts the Y-axis at
  A)
  (0, 13) done clear
  B)
  (0, -13) done clear
  C)
  (0, 12) done clear
  D)
  (13, 0) done clear
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• question_answer38)
  The point......... lies on the perpendicular bisector of the line segment joining the points A (-2, -5) and 5(2, 5).
  A)
  (0, 0) done clear
  B)
  (0, 2) done clear
  C)
  (2, 0) done clear
  D)
  (-2, 0) done clear
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• question_answer39)
  A line intersects the Y-axis and X-axis at the points P and Q, respectively. If (2, - 5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
  A)
  (0, -5) and (2, 0) done clear
  B)
  (0, 10) and (-4, 0) done clear
  C)
  (0, 4) and (-10, 0) done clear
  D)
  (0, -10) and (4, 0) done clear
  View Solution play_arrow

• question_answer40)
  \[\Delta ABC\]with vertices A(-2, 0), B(2, 0) and C(0,2) is similar to \[\Delta DEF\]with vertices \[D\left( -4,\,0 \right),\,E\left( 4,\,0 \right)\]and F (0, 4).
  A)
  True done clear
  B)
  False done clear
  C)
  Can't say done clear
  D)
  Partially True/False done clear
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• question_answer41)
  If (a, b) is the mid-point of the line segment joining the points A(10, -6) and B(k, 4) and a - 2b = 18, then the value of k is
  A)
  30 done clear
  B)
  22 done clear
  C)
  4 done clear
  D)
  40 done clear
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• question_answer42)
  Using section formula, check that the points A (- 3, -1), B (1, 3) and C (-1, 1) are collinear.
  A)
  Yes done clear
  B)
  No done clear
  C)
  Can't say done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer43)
  The ratio, in which the Y-axis divides the line segment joining the points (5, - 6) and (- 1, - 4) is
  A)
  1:5 done clear
  B)
  5:1 done clear
  C)
  2:4 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer44)
  Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2 : 3.
  A)
  (1, 3) done clear
  B)
  (2, 6) done clear
  C)
  (3, 4) done clear
  D)
  (4, 6) done clear
  View Solution play_arrow

• question_answer45)
  The ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8) is
  A)
  2:3 done clear
  B)
  1:2 done clear
  C)
  3:2 done clear
  D)
  2:1 done clear
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• question_answer46)
  If the points A (6,1), B (8, 2), C (9, 4) and D (p, 3) are the vertices of a parallelogram, taken in order, then the value of p is
  A)
  5 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  7 done clear
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• question_answer47)
  The coordinates of point A, where AB is the diameter of a circle whose centre is (3, -4) and B is (1,4) is
  A)
  (2, 0) done clear
  B)
  (12, -5) done clear
  C)
  (5, -12) done clear
  D)
  None of the above done clear
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• question_answer48)
  The coordinates of the point of trisection of the line segment joining (2, - 3) and (4, - 1). (when the point is near the point (2, - 3)) is
  A)
  (10/3,-5/3) done clear
  B)
  (8/3,-7/3) done clear
  C)
  (3,-2) done clear
  D)
  None of the above done clear
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• question_answer49)
  List-II gives the coordinates of the point P that divides the line segment joining the points in the given ratio given in List-I, match them correctly.

  	List - I		List - II
  P.	A(-1, 3) and B (-5, 6) internally in the ratio 1 : 2	1.	(7, 3)
  Q.	A (-2, 1) and B (1, 4) internally in the ratio 2 : 1	2.	(0, 3)
  R.	A (1, 7) and B (3, 4) internally in the ratio 3 : 3	3.	\[\left( \frac{11}{5},\frac{26}{5} \right)\]
  S.	A (4, -3) and B (8, 5) internally in the ratio 3 : 1	4.	\[\left( -\frac{7}{3},\,4 \right)\]

  A)
  P-4,      Q-2,     R-3,     S-1 done clear
  B)
  P-3,      Q-2,     R-4,     S-1 done clear
  C)
  P-1,      Q-4,     R-3,     S-2 done clear
  D)
  P-3,      Q-1,     R-2,     S-4 done clear
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• question_answer50)
  Match the following

  	List - I		List - II
  P.	Distance between (- 6, 7) and (-1, -5) is	1.	- 3, 7
  Q.	The value of k for which the distance between \[A\left( k,\,-5 \right)\] and \[B\left( 2,\,7 \right)\] is 13 units	2.	x + y = 5
  R.	(x, y) is equidistant from (5, 1) and (-1, 5) if	3.	3x = 2y
  S.	(x, y), (2, 3) and (4, 1) are collinear, if	4.	13 units

  A)
  P-3,      Q-4,     R-2,     S-1 done clear
  B)
  P-1,      Q-2,     R-4,     S-3 done clear
  C)
  P-4,      Q-1,     R-3,     S-2 done clear
  D)
  P-3,      Q-2,     R-4,     S-1 done clear
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