RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS

RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS

Other Exercises

Mark the correct alternative in each of the following :
Question 1.
The distance between the points (cosθ, sinθ) and (sinθ, -cosθ) is
(a) √3
(b) √2
(c) 2
(d) 1
Solution:
(b) Distance between (cosθ, sinθ) and (sinθ, -cosθ)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 1
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 2

Question 2.
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
(a) a
(b) 2a
(c) 3a
(d) None of these
Solution:
(a) Distance between (a cos 25°, 0) and (0, a cos 65°)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 3

Question 3.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, -6) is 10 units, then x =
(a) 3
(b) -3
(c) 9
(d) -9
Solution:
(c) Distance between P (x, 2) and Q (3, -6) = 10 units
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 4
=> x (x – 9) + 3 (x – 9) = 0
(x – 9) (x + 3) = 0
Either x – 9 = 0, then x = 9 or x + 3 = 0, then x = -3
x is positive integer
Hence x = 9

Question 4.
The distance between the points (a cosθ + b sinθ, 0) and (0, a sinθ – b cosθ) is
(a) a² + b²
(b) a + b
(c) a² – b²
(d) √(a²+b²)
Solution:
(d) Distance between (a cosθ + b sinθ, 0) and (0, a sinθ – b cosθ)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 5

Question 5.
If the distance between the points (4, p) and (1, 0) is 5, then p =
(a) ±4
(b) 4
(c) -4
(d) 0
Solution:
(a) Distance between (4, p) and (1, 0) = 5
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 6
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 7

Question 6.
A line segment is of length 10 units. If the coordinates of its one end are (2, -3) and the abscissa of the other end is 10, then its ordinate is
(a) 9, 6
(b) 3, -9
(c) -3, 9
(d) 9, -6
Solution:
(b) Let the ordinate of other end = y
then distance between (2, -3) and (10, y) = 10 units
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 8

Question 7.
The perimeter of the triangle formed by the points (0, 0), (1, 0) and (0, 1) is
(a) 1 ± √2
(b) √2 + 1
(c) 3
(d) 2 + √2
Solution:
(d) Let the vertices of ∆ABC be A (0, 0), B(1, 0) and C (0, 1)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 9
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 10

Question 8.
If A (2, 2), B (-4, -4) and C (5, -8) are the vertices of a triangle, then the length of the median through vertices C is
(a) √65
(b) √117
(c) √85
(d) √113
Solution:
(c) Let mid point of A (2, 2), B (-4, -4) be D whose coordinates will be
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 11

Question 9.
If three points (0, 0), (3, √3) and (3, λ) form an equilateral triangle, then λ =
(a) 2
(b) -3
(c) -4
(d) None of these
Solution:
(d) Let the points (0, 0), (3, √3) and (3, λ) from an equilateral triangle
AB = BC = CA
=> AB² = BC² = CA²
Now, AB² = (x2 – x1)² + (y2 – y1
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 12

Question 10.
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
(a) \(\frac { 1 }{ 3 }\)
(b) \(\frac { -1 }{ 3 }\)
(c) \(\frac { 2 }{ 3 }\)
(d) \(\frac { -2 }{ 3 }\)
Solution:
(b) Let the points A (k, 2k), B (3k, 3k) and C (3, 1) be the vertices of a ∆ABC
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 13
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 14

Question 11.
The coordinates of the point on x-axis which are equidistant from the points (-3, 4) and (2, 5) are
(a) (20, 0)
(b) (-23, 0)
(c) (\(\frac { 4 }{ 5 }\) , 0)
(d) None of these
Solution:
(d)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 15

Question 12.
If (-1, 2), (2, -1) and (3, 1) are any three vertices of a parallelogram, then
(a) a = 2, b = 0
(b) a = -2, b = 0
(c) a = -2, b = 6
(d) a = 0, b = 4
Solution:
(d) In ||gm ABCD, diagonals AC and AD bisect each other at O
O is mid-point of AC
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 16

Question 13.
If A (5, 3), B (11, -5) and P (12, y) are the vertices of a right triangle right angled at P, then y =
(a) -2, 4
(b) -2, 4
(c) 2, -4
(d) 2, 4
Solution:
(c) A (5, 3), B (11, -5) and P (12, y) are the vertices of a right triangle, right angle at P
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 17
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 18

Question 14.
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b) is
(a) a + b + c
(b) abc
(c) (a + b + c)²
(d) 0
Solution:
(d) Vertices of a triangle are (a, b + c), (b, c + a) and (c, a + b)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 19

Question 15.
If (x, 2), (-3, -4) and (7, -5) are coliinear, then x =
(a) 60
(b) 63
(c) -63
(d) -60
Solution:
(c) Area of triangle whose vertices are (x, 2), (-3, -4) and (7, -5)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 20
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 21

Question 16.
If points (t, 2t), (-2, 6) and (3, 1) are collinear, then t =
(a) \(\frac { 3 }{ 4 }\)
(b) \(\frac { 4 }{ 3 }\)
(c) \(\frac { 5 }{ 3 }\)
(d) \(\frac { 3 }{ 5 }\)
Solution:
(b) The area of triangle whose vertices are (t, 2t), (-2, 6) and (3, 1)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 22

Question 17.
If the area of the triangle formed by the points (x, 2x), (-2, 6) and (3, 1) is 5 square units, then x =
(a) \(\frac { 2 }{ 3 }\)
(b) \(\frac { 3 }{ 5 }\)
(c) 2
(d) 5
Solution:
(c) Area of triangle whose vertices are (x, 2x), (-2, 6) and (3, 1)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 23

Question 18.
If points (a, 0), (0, b) and (1, 1) are collinear, then \(\frac { 1 }{ a }\) + \(\frac { 1 }{ b }\) =
(a) 1
(b) 2
(c) 0
(d) -1
Solution:
(a) The area of triangle whose vertices are (a, 0), (0, b) and (1, 1)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 24
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 25

Question 19.
If the centroid of a triangle is (1, 4) and two of its vertices are (4, -3) and (-9, 7), then the area of the triangle is
(a) 183 sq. units
(b) \(\frac { 183 }{ 2 }\) sq. units
(c) 366 sq. units
(d) \(\frac { 183 }{ 4 }\) sq. units
Solution:
(b) Centroid of a triangle = (1, 4)
and two vertices of the triangle are (4, -3) and (-9, 7)
Let the third vertex be (x, y), then
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 26
= \(\frac { 183 }{ 2 }\) sq. units

Question 20.
The line segment joining points (-3, -4) and (1, -2) is divided by y-axis in the ratio
(a) 1 : 3
(b) 2 : 3
(c) 3 : 1
(d) 2 : 3
Solution:
(c) The point lies on y-axis
Its abscissa will be zero
Let the point divides the line segment joining the points (-3, -4) and (1, -2) in the ratio m : n
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 27

Question 21.
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
(a) -2 : 3
(b) -3 : 2
(c) 3 : 2
(d) 2 : 3
Solution:
(d) Let the point (4, 5) divides the line segment joining the points (2, 3) and (7, 8) in the ratio m : n
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 28

Question 22.
The ratio in which the X-axis divides the segment joining (3, 6) and (12, -3) is
(a) 2 : 1
(b) 1 : 2
(c) -2 : 1
(d) 1 : -2
Solution:
(a) The point lies on x-axis
Its ordinate is zero
Let this point divides the line segment joining the points (3, 6) and (12, -3) in the ratio m : n
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 29

Question 23.
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
(a) abc
(b) 0
(c) a + b + c
(d) 3 abc
Solution:
(d) Centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is origin (0, 0)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 30

Question 24.
If points (1, 2), (-5, 6) and (a, -2) are collinear, then a =
(a) -3
(b) 7
(c) 2
(d) -2
Solution:
(b) The area of a triangle whose vertices are (1, 2), (-5, 6) and (a, -2)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 31
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 32

Question 25.
If the centroid of the triangle formed by (7, x), (y, -6) and (9, 10) is at (6, 3), then (x, y) =
(a) (4, 5)
(b) (5, 4)
(c) (-5, -2)
(d) (5, 2)
Solution:
(d) Centroid of (7, x), (y, -6) and (9, 10) is (6, 3)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 33

Question 26.
The distance of the point (4, 7) from the x-axis is
(a) 4
(b) 7
(c) 11
(d) √65
Solution:
(b) The distance of the point (4, 7) from x-axis = 7

Question 27.
The distance of the point (4, 7) from the y-axis is
(a) 4
(b) 7
(c) 11
(d) √65
Solution:
(a) The distance of the point (4, 7) from y-axis = 4

Question 28.
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are
(a) (0, 3)
(b) (3, 0)
(c) (0, 0)
(d) (0, -3)
Solution:
(a) P is a point on x-axis and its distance from 0 is 3
Co-ordinates of P will be (3, 0)
Q is a point on OY such that OP = OQ
Co-ordinates of Q will be (0, 3)

Question 29.
If the point (x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
(a) ±5
(b) ±3
(c) 0
(d) ±4
Solution:
(b) Point A (x, 4) is on a circle with centre O (0, 0) and radius = 5
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 34

Question 30.
If the point P (x, y) is equidistant from A (5, 1) and B (-1, 5), then
(a) 5x = y
(b) x = 5y
(c) 3x = 2y
(d) 2x = 3y
Solution:
(c)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 35

Question 31.
If points A (5, p), B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
(a) 7
(b) 3
(c) 6
(d) 8
Solution:
(c) Vertices of a square are A (5, p), B (1, 5), C (2, 1) and D (6, 2)
The diagonals bisect each other at O
O is the mid-point of AC and BD
O is mid-point of BD, then
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 36

Question 32.
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b) are
(a) (a, b)
(b) (\(\frac { a }{ 2 }\) , \(\frac { b }{ 2 }\))
(c) (\(\frac { b }{ 2 }\) , \(\frac { a }{ 2 }\))
(d) (b, a)
Solution:
(b) Let co-ordinates of C be (x, y) which is the centre of the circumcircle of ∆OAB
Radii of a circle are equal
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 37
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 38

Question 33.
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (-3, 4) are
(a) (0, 2)
(b) (3, 0)
(b) (0, 3)
(d) (2, 0)
Solution:
(d) The given point P lies on x-axis
Let the co-ordinates of P be (x, 0)
The point P lies on the perpendicular bisector of of the line segment joining the points A (7, 6), B (-3, 4)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 39

Question 34.
If the centroid of the triangle formed by the points (3, -5), (-7, 4), (10, -k) is at the point (k, -1), then k =
(a) 3
(b) 1
(c) 2
(d) 4
Solution:
(c) O (k, -1) is the centroid of triangle whose vertices are
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 40

Question 35.
If (-2, 1) is the centroid of the triangle having its vertices at (x, 0), (5, -2), (-8, y), then x, y satisfy the relation
(a) 3x + 8y = 0
(b) 3x – 8y = 0
(c) 8x + 3y = 0
(d) 8x = 3y
Solution:
(-2, 1) is the centroid of triangle whose vertices are (x, 0), (5, -2), (-8, y)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 41

Question 36.
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
(a) (3, 0)
(b) (0, 2)
(c) (-2, 3)
(d) (3, 2)
Solution:
(c) Three vertices of a rectangle are A (0, 0), B (2, 0), C (0, 3)
Let fourth vertex be D (x, y)
The diagonals of a rectangle bisect eachother at O
O is the mid-point of AC, then
Coordinates of O will be (\(\frac { 0+0 }{ 2 }\) , \(\frac { 0+3 }{ 2 }\))
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 42

Question 37.
The length of a line segment joining A (2, -3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
(a) 3 or -9
(b) -3 or 9
(c) 6 or 27
(d) -6 or-27
Solution:
(a) Abscissa of B is 10 and co-ordinates of A are (2, -3)
Let ordinates of B be y, then
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 43

Question 38.
The ratio in which the line segment joining P(x1, y1) and Q (x2, y2) is divided by x-axis is
(a) y1 : y2
(b) -y1 : y2
(c) x1 : x2
(d) -x1 : x2
Solution:
(b) Let a point A on x-axis divides the line segment joining the points P (x1, y1), Q (x2, y2) in the ratio m1 : m2 and
let co-ordinates of A be (x, 0)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 44

Question 39.
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
(a) -a1 : a2
(b) a1 : a2
(c) b1 : b2
(d) -b1 : b2
Solution:
(a) Let the point P on y-axis, divides the line segment joining the point A (a1, b1) and B (a2, b2) is the ratio m1 : m2 and
let the co-ordinates of P be (0, y), then
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 45

Question 40.
If the line segment joining the points (3, -4) and (1, 2) is trisected at points P
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 46
Solution:
(b)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 47
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 48

Question 41.
If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are [CBSE 2012]
(a) (-6, 7)
(b) (6, -7)
(c) (6, 7)
(d) (-6, -7)
Solution:
(a) Let AB be the diameter of a circle with centre O
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 49

Question 42.
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are
(a) (2, 4)
(b) (3, 5)
(c) (4, 2)
(d) (5, 3) [CBSE 2012]
Solution:
(b) Point P divides the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1
Let coordinates of P be (x, y), then
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 50

Question 43.
In the figure, the area of ∆ABC (in square units) is [CBSE 2013]
(a) 15
(b) 10
(c) 7.5
(d) 2.5
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 51
Solution:
(c)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 52

Question 44.
The point on the x-axis which is equidistant from points (-1, 0) and (5, 0) is
(a) (0, 2)
(b) (2, 0)
(c) (3, 0)
(d) (0, 3) [CBSE 2013]
Solution:
(c) Let the point P (x, 0) is equidistant from the points A (-1, 0), B (5, 0)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 53

Question 45.
If A (4, 9), B (2, 3) and C (6, 5) are the vertices of ∆ABC, then the length of median through C is
(a) 5 untis
(b) √10 units
(c) 25 units
(d) 10 units [CBSE 2014]
Solution:
(b) A (4, 9), B (2, 3) and C (6, 5) are the vertices of ∆ABC
Let median CD has been drawn C (6, 5)
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 54

Question 46.
If P (2, 4), Q (0, 3), R (3, 6) and S (5, y) are the vertices of a paralelogram PQRS, then the value of y is
(a) 7
(b) 5
(c) -7
(d) -8 [CBSE 2014]
Solution:
(a) P (2, 4), Q (0, 3), R (3, 6) and S (5, y) are the vertices of a ||gm PQRS
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 55
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 56

Question 47.
If A (x, 2), B (-3, -4) and C (7, -5) are collinear, then the value of x is
(a) -63
(b) 63
(c) 60
(d) -60 [CBSE 2014]
Solution:
(a) A (x, 2), B (-3, -4) and C (7, -5) are collinear, then area ∆ABC = 0
Now area of ∆ABC
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 57

Question 48.
The perimeter of a triangle with vertices (0, 4) and (0, 0) and (3, 0) is
(a) 7 + √5
(b) 5
(c) 10
(d) 12 [CBSE 2014]
Solution:
(d) A (0, 4) and B (0, 0) and C (3, 0) are the vertices of ∆ABC
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 58

Question 49.
If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then
(a) AP = \(\frac { 1 }{ 3 }\) AB
(b) AP = BP
(c) BP = \(\frac { 1 }{ 3 }\) AB
(d) AP = \(\frac { 1 }{ 2 }\) AB
Solution:
(d) Given that, the point P (2, 1) lies on the line segment joining the points (4, 2) and B (8, 4), which shows in the figure below:
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 59
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 60

Question 50.
A line intersects the y-axis and x-axis at 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)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
Solution:
(d) Let the coordinates of P and Q (0, y) and (x, 0), respectively.
So, the mid-point of P (0, y) and Q (x, 0) is
RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS 61
2 = \(\frac { x + 0 }{ 2 }\) and -5 = \(\frac { y + 0 }{ 2 }\)
=> 4 = x and -10 = y
=> x = 4 and y = -10
So, the coordinates of P and Q are (0, -10) and (4, 0).

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