## MCQ for Class 10 Mathematics Coordinate Geometry

Class 10 Mathematics students should refer to the following multiple-choice questions with answers for Coordinate Geometry in standard 10. These MCQ questions with answers for Grade 10 Mathematics will come in exams and help you to score good marks

### Coordinate Geometry MCQ Questions Class 10 Mathematics with Answers

**Question : 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, the value of k is:**

(a) 40

(b) 22

(c) 4

(d) 36**Answer : B**

**Question : Point A (-1, y) and B (5, 7) lie on a circle with centre O (2, -3y). The values of y are:**

(a) 1, -7

(b) -2, 7

(c) -2, -7

(d) -1, 7**Answer : D**

**Question : The distance between the points (a cos 𝜃 + b sin 𝜃, 0) and (0, a sin 𝜃 - b cos 𝜃), is :**

(a) √𝑎^{2} − 𝑏^{2}

(b) 𝑎^{2} + 𝑏^{2}

(c) 𝑎^{2} − 𝑏^{2}

(d) √𝑎^{2} + 𝑏^{2}**Answer : D**

**Question : Distance between two points (3, 2) and (6, 6) is:**

(a) 5

(b) 3

(c) 2

(d) 8**Answer : A**

**Question : If the point P (k, 0) divides the line segment joining the points A (2, -2) and B (-7, 4) in the ratio 1:2, then the value of k is :**

(a) 1

(b) 2

(c) -1

(d) -2**Answer : C**

**Question : The point P on x- axis is equidistant from the points A (-1, 0) and B (5, 0) is:**

(a) (2, 2)

(b) (0, 2)

(c) (2, 0)

(d) (3, 2)**Answer : C**

**Question : If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is :**

(a) 4

(b) 2

(c) 1

(d) 3**Answer : C**

**Question : The line segment joining the points P (-3, 2) and Q (5, 7) is divided by the y- axis in the ratio:**

(a) 3 : 1

(b) 3 : 2

(c) 3 : 4

(d) 3 : 5**Answer : D**

**Question : The distance of the point P (-6, 8) from the origin is:**

(a) 14

(b) 6

(c) 8

(d) 10**Answer : D**

**Question : The mid-point of the line segment joining the points A (-2, 8) and B (-6,-4) is:**

(a) (-4, -6)

(b) (-4, 2)

(c) (2, 6)

(d) (6, -2)**Answer : B**

**Question : The distance of the point P(2, 3) from the x-axis is**

(a) 2

(b) 3

(c) 1

(d) 5**Answer : B**

**Question : The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is **

(a) 3

(b) 2

(c) 1

(d) -1**Answer : D**

**Question : The distance between the point P(1, 4) and Q(4, 0) is **

(a) 4

(b) 5

(c) 6

(d) 3√3**Answer : B**

**Question : If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is **

(a) -7 or -1

(b) -7 or 1

(c) 7 or 1

(d) 7 or -1**Answer : D**

**Question : 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**Answer : C**

**Question : If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then **

(a) 2a = b

(b) a = -b

(c) a = 2b

(d) a = b**Answer : A**

**Question : The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio **

(a) 3 : 4

(b) 3 : 2

(c) 2 : 3

(d) 4 : 3**Answer : A**

**Question : The points (1,1), (-2, 7) and (3, -3) are **

(a) vertices of an equilateral triangle

(b) collinear

(c) vertices of an isosceles triangle

(d) none of these**Answer : B**

**Question : If the points A(4,3) and B (x,5) are on the circle with centre O(2,3), then the value of x is :**

(a) 5

(b) 6

(c) 2

(d) 0**Answer : D**

**Question : If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is **

(a) 12

(b) -6

(c) -12

(d) -4**Answer : C**

**Question : The ratio in which the segment joining the points (5, 1) and (–7, –1) divided by x-axis is :**

**Answer : D**

**Question : The coordinates of the points of trisection of a segment joining A(–3, 2) and B(9, 5) is :**

**Answer : D**

**Question : If A (3, 1), B(2, 6) and C(–5. 7) are the midpoints of the sides of △PQR, then the area of the △PQR is :**

**Answer : A**

**Question : A(–1, 2), B(4, 1) and C(7, 6) are three vertices of the parallelogram ABCD. Then the coordinates of fourth vertex is :**

**Answer : D**

**Question : The ratio in which the line 3x + y – 9 =0 divides the line segment joining the points A(1, 3) and B(2, 7) is**

**Answer : D**

**Question : The coordinates of a point P on y-axis, equidistant from two points A(–5, –2) and B(3, 2) on the same plane are :**

**Answer : B**

**Question : If A(1, 4), B(3, 0) and C(2, 1) are the vertices of a triangle, then the length of the median through C is**

**Answer : A**

**Question : (2a, 4a), (2a, 6a) and (2a + 3 a, 5a) are the vertices of :**

**Answer : C**

**Question : If A (1, 1) and B(2, –3) are two points and P is a point on AB produced such that AP = 3AB. Then the co-ordinate of point P are :**

**Answer : B**

**Question : If point P divides the line joining A(–3, 3) and B(2, –7) internally in the ratio 2 : 3, then the coordinates of point P are :**

**Answer : D**

**CASE STUDY-1**

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is.

The left-right (horizontal) direction is commonly called X-axis.

The up-down (vertical) direction is commonly called Y-axis.

When we include negative values, the x and y axes divide the space up into 4 pieces.

Read the information given above and below and answer the questions that follow:

Two friends Seema and Aditya work in the same office in Delhi. In the Christmas vacations, both decided to go their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure) in Delhi.

**(i) Who will travel more distance to reach their home?Answer : **Aditya

**(ii) Find the location of the stationAnswer : **(-4, 4)

**(iii) Find in which ratio Y-axis divide Town B and Station.Answer : **1: 1

**CASE STUDY - 2**

Karan went to the Lab near to his home for COVID 19 test along with his family members.

The seats in the waiting area were as per the norms of distancing during this pandemic (as shown in the above figure). His family member took their seats surrounded by red circular area.

**(i) What is the distance between Neena and Karan?Answer : **√10

**(ii) What are the coordinates of seat of Akash?Answer :** (2, 3)

**(iii) What will be the coordinates of a point exactly between Akash and Binu where a person can beAnswer : **(3.5, 2.5)

**Question : The points A(0, –2), B(3, 1), C(0, 4) and D(–3, 1) are the vertices of a**

(a) parallelogram

(b) rectangle

(c) square

(d) rhombus

**Question : If A(3, 8), B(4, –2) and C(5, –1) are the vertices of ΔABC. Then, its area is**

(a) 28(1/2)sq. units

(b) 37(1/2)sq. units

(c) 57sq. units

(d) 75 sq. units

**Question : The points A(0, 6), B(–5, 3) and C(3, 1) are the vertices of a triangle which is**

(a) isosceles

(b) equilateral

(c) scalene

(d) right angled

**Question : Two vertices of ΔABC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). The coordinate of C is**

(a) (4, 3)

(b) (4, 15)

(c) (–4, –15)

(d) (–15, –4)

**Question : The coordinates of the centroid of ABC with vertices A(–1, 0), B(5, –2) and C(8, 2) is**

(a) (12, 0)

(b) (6, 0)

(c) (0, 6)

(d) (4, 0)

**Question : If the points A(2, 3), B(5, k) and C(6, 7) are collinear, then the value of k is**

(a) 4

(b) 6

(c) -3 /2

(d) 11 /4

**Question : If P(–1, 1) is the middle point of the line segment joining A(–3, b) and B(1, b + 4) then the value of b is**

(a) 1

(b) –1

(c) 2

(d) 0

**Question : y–axis divides the join of P(–4, 2) and Q(8, 3) in the ratio**

(a) 3 : 1

(b) 1 : 3

(c) 2 : 1

(d) 1 : 2

**Question : x–axis divides the join of A(2, –3) and B(5, 6) in the ratio**

(a) 3 : 5

(b) 2 : 3

(c) 2 : 1

(d) 1 : 2

**Question : The point P(1, 2) divides the join of A(–2, 1) and B(7, 4) are in the ratio of**

(a) 3 : 2

(b) 2 : 3

(c) 2 : 1

(d) 1 : 2

**Question : A point P divides the join of A(5, –2) and B(9, 6) are in the ratio 3 : 1. The coordinates of P are**

(a) (4, 7)

(b) (8, 4)

(c) ( 11/2, 5)

(d) (12, 8)

**Question : What point on x – axis is equidistant from the points A(7, 6) and B(–3, 4)?**

(a) (0, 4)

(b) (–4, 0)

(c) (3, 0)

(d) (0, 3)

**Question : The distance of the point P(4, –3) from the origin is**

(a) 1 unit

(b) 7 units

(c) 5 units

(d) 3 units

**Question : The distance between the points A(2, –3) and B(2, 2) is**

(a) 2 units

(b) 4 units

(c) 5 units

(d) 3 units

**Question : Find the area of the triangle whose vertices are A(1, 2), B(–2, 3) and C(–3, –4)**

(a) 11sq. units

(b) 22 sq. units

(c) 7 sq. units

(d) 6.5 sq. units

**Question : Find the area of the triangle whose vertices are A(2, 4), B(–3, 7) and C(–4, 5)**

(a) 11sq. units

(b) 22 sq. units

(c) 7 sq. units

(d) 6.5 sq. units

**Question : Find the area of the triangle whose vertices are A(10, –6), B(2, 5) and C(–1, 3)**

(a) 12.5 sq. units

(b) 24.5 sq. units

(c) 7 sq. units

(d) 6.5 sq. units

**Question : Find the area of the triangle whose vertices are A(4, 4), B(3, –16) and C(3, –2)**

(a) 12.5 sq. units

(b) 24.5 sq. units

(c) 7 sq. units

(d) 6.5 sq. units

**Question : For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?**

(a) 1

(b) –1

(c) 2

(d) –2

**Question : For what value of y are the points A(1, 4), B(3, y) and C(–3, 16) collinear?**

(a) 1

(b) –1

(c) 2

(d) –2

**Question : Find the value of p for which the points A(–1, 3), B(2, p) and C(5, –1) collinear?**

(a) 1

(b) –1

(c) 2

(d) –2

**Question : What is the midpoint of a line with endpoints (–3, 4) and (10, –5)?**

(a) (–13, –9)

(b) (–6.5, –4.5)

(c) (3.5, –0.5)

(d) none of these

**Question : A straight line is drawn joining the points (3, 4) and (5,6). If the line is extended, the ordinate of the point on the line, whose abscissa is –1 is**

(a) 1

(b) –1

(c) 2

(d) 0

**Question : If the distance between the points (8, p) and (4, 3) is 5 then value of p is**

(a) 6

(b) 0

(c) both (a) and (b)

(d) none of these

**Question : The fourth vertex of the rectangle whose three vertices taken in order are (4,1), (7, 4), (13, –2) is**

(a) (10, –5)

(b) (10, 5)

(c) (8, 3)

(d) (8, –3)

**Question : If four vertices of a parallelogram taken in order are (–3, –1), (a, b), (3, 3) and (4, 3). Then a : b =**

(a) 1 : 4

(b) 4 : 1

(c) 1 : 2

(d) 2 : 1

**Question : Area of the triangle formed by (1, – 4), (3, – 2) and (– 3,16) is**

(a) 40 sq. units

(b) 48 sq. units

(c) 24 sq. units

(d) none of these

**Question : The points (2, 5), (4, - 1), (6, - 7) are vertices of an ___________ triangle**

(a) isosceles

(b) equilateral

(c) scalene

(d) right angled

**Question : The area of triangle formed by the points (p, 2 - 2p), (l-p,2p) and (-4-p, 6- 2p) is 70 sq. units. How many integral value of p are possible ?**

(a) 2

(b) 3

(c) 4

(d) none of these

**Question : If the origin is the mid-point of the line segment joined by the points (2,3) and (x,y), then the value of (x,y) is**

(a) (2, –3)

(b) (2, 3)

(c) (–2, 3)

(d) (–2, –3)

**Question : The distance of the point P(2, 3) from the x-axis is:**

(a) 2

(b) 3

(c) 1

(d) 5

**Question : The distance between the points A(0, 6) and B(0, -2) is:**

(a) 2

(b) 6

(c) 4

(d) 8

**Question : The distance of the point P(-6, 8) from the origin is:**

(a) 8

(b) 27

(c) 10

(d) 6

**Question : The distance between the points (0, 5) and (-5, 0) is:**

(a) 5

(b) 52

(c) 25

(d) 10

**Question : AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is:**

(a) 5

(b) 3

(c) 34

(d) 4

**Question : The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is:**

(a) 5

(b) 12

(c) 11

(d) 7 + 5

**Question : The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is:**

(a) 14

(b) 28

(c) 8

(d) 6

**Question : The points (–4, 0), (4, 0), (0, 3) are the vertices of a :**

(a) Right triangle

(b) Isosceles triangle

(c) Equilateral triangle

(d) Scalene triangle

**Question : Point on x – axis has coordinates:**

(a) (a, 0)

(b) (0, a)

(c) (–a, a)

(d) (a, –a)

**Question : Point on y – axis has coordinates:**

(a) (–a, b)

(b) (a, 0)

(c) (0, b)

(d) (–a, –b)

**Question : Line formed by joining (- 1,1) and (5, 7) is divided by a line x + y = 4 in the ratio of**

(a) 1 : 4

(b) 1 : 3

(c) 1 : 2

(d) 3 : 4

**Question : If the area of the triangle with vertices (x, 0), (1,1) and (0, 2) is 4 square units, then a value of x is**

(a) –2

(b) –4

(c) –6

(d) 8

**Question : Point A(–5, 6) is at a distance of:**

(a) 61 units from the origin

(b) 11 units from the origin

(c) √61 units from the origin

(d) √11 units from the origin

**Question : If the points (1, x), (5, 2) and (9, 5) are collinear then the value of x is**

(a) 5/2

(b) -5/2

(c) –1

(d) 1

**Question : The end points of diameter of circle are (2, 4) and (–3, –1). The radius of the circle us**

(a) 5√2/2

(b) 5√2

(c) 3√2

(d) 15√2/2

**Question : The ratio in which x – axis divides the line segment joining the points (5, 4) and (2, –3) is:**

(a) 5 : 2

(b) 3 : 4

(c) 2 : 5

(d) 4 : 3

**Question : 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

(b) II quadrant

(c) III quadrant

(d) IV quadrant

**Question : The point which lies on the perpendicular bisector of the line segment joining the points A(–2, – 5) and B(2, 5) is:**

(a) (0, 0)

(b) (0, 2)

(c) (2, 0)

(d) (–2, 0)

**Question : The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8,3) is:**

(a) (0, 1)

(b) (0, -1)

(c) (-1, 0)

(d) (1, 0)

**Question : If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then**

**Question : Three vertices of a parallelogram taken in order are (- 1, - 6), (2, - 5) and (7, 2). The fourth vertex is**

(a) (1, 4)

(b) (1, 1)

(c) (4, 4)

(d) (4, 1)

**Question : If A and B are the points ( - 3, 4) and (2,1) respectively, then the coordinates of the points on AB produced such that AC = 2BC are**

(a) (2, 4)

(b) (3, 7)

(c) (7, –2)

(d) none of these

**Question : Distance of the point (4, a) from x-axis is half its distance from y-axis then a =**

(a) 2

(b) 8

(c) 4

(d) 6

**Question : A triangle is formed by the points 0(0, 0), A(5,0) and B(0,5). The number of points having integral coordinates (both x and y) and strictly inside the triangle is**

(a) 10

(b) 17

(c) 16

(d) 6

**Question : If P(l, 2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelogram PQRS then**

(b) a = 3, b = 4

(c) a = 2, b = 3

(d) a = 3, b = 5

**Question : The number of points on x-axis which are at a distance of 2 units from (2, 4) is**

(b) 1

(c) 3

(d) 0

**Question : The distance of the point (h, k) from x-axis is**

(b) k

(c) | h |

(d) | k |

**Question : The vertices of a triangle are (0, 0), (3, 0) and (0, 4). Its orthocentre is at**

(b) (4, 0)

(c) (0, 0)

(d) (3, 4)

**Question : The area of the triangle with vertices at the points (a, b + c), (b, c + a) and (c, a + b) is**

(b) a + b – c

(c) a – b + c

(d) 0

**Question : If the segment joining the points (a, b) and (c, d) subtends a right angle at the origin, then**

(b) ac + bd = 0

(c) ab – cd = 0

(d) ab + cd = 0

**Question : The distance of A(5, -12) from the origin is**

(b) 11

(c) 13

(d) 10

**Question : Find the ordinate of a point whose abscissa is 10 and which is at a distance of 10 units from the point P(2, -3).**

(b) –9

(c) both (a) or (b)

(d) none of these

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