Class 10 Maths · Chapter 7

Coordinate Geometry

112 Class 10 Maths questions on Coordinate Geometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 6

1. Q21 Exemplar · Exercise 7.1
   The distance ​of ​the point $P(2,3)$ from ​the $x$-axis ​is

   1. (a)$2$
   2. (b)$3$
   3. (c)$1$
   4. (d)$5$
   Show answer

   (b) $3$

   Step-by-step solution →
2. Q22 Exemplar · Exercise 7.1
   The ​distance between ​the points $A(0,6)$ and $B(0,-2)$ ​is

   1. (a)6
   2. (b)8
   3. (c)4
   4. (d)2
   Show answer

   (b) 8

   Step-by-step solution →
3. Q23 Exemplar · Exercise 7.1
   The ​distance of ​the ​point $P(-6,8)$ from ​the ​origin is

   1. (a)8
   2. (b)$2\sqrt{7}$
   3. (c)10
   4. (d)6
   Show answer

   (c) 10

   Step-by-step solution →
4. Q24 Exemplar · Exercise 7.1
   The ​distance ​between ​the ​points $(0,5)$ and $(-5,0)$ is

   1. (a)$5$
   2. (b)$5\sqrt{2}$
   3. (c)$2\sqrt{5}$
   4. (d)$10$
   Show answer

   (b) $5\sqrt{2}$

   Step-by-step solution →
5. Q25 Exemplar · Exercise 7.1
   AOBC ​is a rectangle whose three vertices ​are vertices $A(0,3)$, $O(0,0)$ and $B(5,0)$. The length ​of ​its ​diagonal ​is

   1. (a)5
   2. (b)3
   3. (c)$\sqrt{34}$
   4. (d)4
   Show answer

   (c) $\sqrt{34}$

   Step-by-step solution →
6. Q26 Exemplar · Exercise 7.1
   The ​perimeter of a triangle ​with ​vertices $(0,4)$, $(0,0)$ ​and $(3,0)$ is

   1. (a)$5$
   2. (b)$12$
   3. (c)$11$
   4. (d)$7+\sqrt{5}$
   Show answer

   (b) $12$

   Step-by-step solution →
7. Q27 Exemplar · Exercise 7.1
   The area ​of ​a ​triangle ​with vertices $A(3,0)$, $B(7,0)$ ​and $C(8,4)$ is

   1. (a)$14$
   2. (b)$28$
   3. (c)$8$
   4. (d)$6$
   Show answer

   (c) $8$

   Step-by-step solution →
8. Q28 Exemplar · Exercise 7.1
   The ​points $(-4,0)$, $(4,0)$, $(0,3)$ ​are the ​vertices of ​a

   1. (a)right triangle
   2. (b)isosceles triangle
   3. (c)equilateral triangle
   4. (d)scalene triangle
   Show answer

   (b) isosceles triangle

   Step-by-step solution →
9. Q29 Exemplar · Exercise 7.1
   The point which divides the ​line segment ​joining ​the points $(7,-6)$ and $(3,4)$ ​in ​ratio $1:2$ ​internally lies ​in the

   1. (a)I quadrant
   2. (b)II quadrant
   3. (c)III quadrant
   4. (d)IV quadrant
   Show answer

   (d) IV quadrant

   Step-by-step solution →
10. Q30 Exemplar · Exercise 7.1
    The point which ​lies ​on the perpendicular ​bisector ​of ​the line ​segment joining the ​points $A(-2,-5)$ and $B(2,5)$ is

    1. (a)$(0,0)$
    2. (b)$(0,2)$
    3. (c)$(2,0)$
    4. (d)$(-2,0)$
    Show answer

    (a) $(0,0)$

    Step-by-step solution →
11. Q31 Exemplar · Exercise 7.1
    The fourth ​vertex ​D ​of ​a ​parallelogram ​ABCD whose three vertices are $A(-2,3)$, $B(6,7)$ and $C(8,3)$ ​is

    1. (a)$(0,1)$
    2. (b)$(0,-1)$
    3. (c)$(-1,0)$
    4. (d)$(1,0)$
    Show answer

    (b) $(0,-1)$

    Step-by-step solution →
12. Q32 Exemplar · Exercise 7.1
    If ​the point $P(2,1)$ lies on the ​line ​segment ​joining points $A(4,2)$ and $B(8,4)$, then

    1. (a)$AP=\frac{1}{3}AB$
    2. (b)$AP=PB$
    3. (c)$PB=\frac{1}{3}AB$
    4. (d)$AP=\frac{1}{2}AB$
    Show answer

    (d) $AP=\frac{1}{2}AB$

    Step-by-step solution →
13. Q33 Exemplar · Exercise 7.1
    If $P\left(\frac{a}{3},4\right)$ ​is the mid-point of the line ​segment joining ​the ​points $Q(-6,5)$ and $R(-2,3)$, then the ​value of $a$ ​is

    1. (a)$-4$
    2. (b)$-12$
    3. (c)$12$
    4. (d)$-6$
    Show answer

    (b) $-12$

    Step-by-step solution →
14. Q34 Exemplar · Exercise 7.1
    The ​perpendicular bisector of ​the ​line segment joining ​the points ​A $(1,5)$ ​and B $(4,6)$ ​cuts the $y$-axis ​at

    1. (a)$(0,13)$
    2. (b)$(0,-13)$
    3. (c)$(0,12)$
    4. (d)$(13,0)$
    Show answer

    (a) $(0,13)$

    Step-by-step solution →
15. Q35 Exemplar · Exercise 7.1
    The coordinates of the point which is equidistant ​from the ​three vertices of the $△AOB$ ​as ​shown ​in Fig. 7.1 is

    1. (a)$(x,y)$
    2. (b)$(y,x)$
    3. (c)$\left(\frac{x}{2},\frac{y}{2}\right)$
    4. (d)$\left(\frac{y}{2},\frac{x}{2}\right)$
    Show answer

    (a) $(x,y)$

    Step-by-step solution →
16. Q36 Exemplar · Exercise 7.1
    A ​circle drawn with origin as the ​centre passes through $\left(\frac{13}{2},0\right)$. The point which does ​not ​lie in the ​interior of ​the ​circle ​is

    1. (a)$\left(-\frac{3}{4},1\right)$
    2. (b)$\left(2,\frac{7}{3}\right)$
    3. (c)$\left(5,-\frac{1}{2}\right)$
    4. (d)$\left(-6,\frac{5}{2}\right)$
    Show answer

    (d) $\left(-6,\frac{5}{2}\right)$

    Step-by-step solution →
17. Q37 Exemplar · Exercise 7.1
    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

    1. (a)$(0,-5)$ and $(2,0)$
    2. (b)$(0,10)$ and $(-4,0)$
    3. (c)$(0,4)$ and $(-10,0)$
    4. (d)$(0,-10)$ and $(4,0)$
    Show answer

    (d) $(0,-10)$ and $(4,0)$

    Step-by-step solution →
18. Q38 Exemplar · Exercise 7.1
    The ​area ​of a ​triangle ​with ​vertices $(a,b+c)$, $(b,c+a)$ ​and $(c,a+b)$ is

    1. (a)$(a+b+c{)}^2$
    2. (b)$0$
    3. (c)$a+b+c$
    4. (d)$abc$
    Show answer

    (b) $0$

    Step-by-step solution →
19. Q39 Exemplar · Exercise 7.1
    If the distance between ​the ​points $(4,p)$ ​and $(1,0)$ is 5, then ​the ​value ​of $p$ is

    1. (a)4 only
    2. (b)$\pm 4$
    3. (c)-4 only
    4. (d)0
    Show answer

    (b) $\pm 4$

    Step-by-step solution →
20. Q40 Exemplar · Exercise 7.1
    If ​the points $A(1,2)$, $O(0,0)$ and $C(a,b)$ ​are collinear, ​then

    1. (a)$a=b$
    2. (b)$a=2b$
    3. (c)$2a=b$
    4. (d)$a=-b$
    Show answer

    (c) $2a=b$

    Step-by-step solution →