Class 10 Maths · Chapter 7

Coordinate Geometry

440 Class 10 Maths questions on Coordinate Geometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 14 of 22

1. Q261 CBSE 2023
   The ​point which lies ​on the ​perpendicular bisector of ​the line segment joining ​the points $A(-3,-4)$ ​and $B(3,4)$ is :

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

   (a) $(0,0)$

   Step-by-step solution →
2. Q262 CBSE 2023
   The distance ​between ​the ​points $(c,0)$ ​and $(0,-c)$ ​is:

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

   (a) $c\sqrt{2}$ units

   Step-by-step solution →
3. Q263 CBSE 2023
   If $(2,4)$ is ​the ​mid-point of ​the ​line-segment joining $(6,3)$ and $(a,5)$, ​then ​the value of $a$ is

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

   (d) $-2$

   Step-by-step solution →
4. Q264 CBSE 2023
   The ​distance ​between ​the ​points $(0,2\sqrt{5})$ and $(-2\sqrt{5},0)$ ​is

   1. (a)$2\sqrt{10}$ units
   2. (b)$4\sqrt{10}$ units
   3. (c)$2\sqrt{20}$ units
   4. (d)$0$
   Show answer

   (a) $2\sqrt{10}$ units

   Step-by-step solution →
5. Q265 CBSE 2023
   The ​distance ​of the point $(-6,8)$ ​from ​origin is ​:

   1. (a)$6$
   2. (b)$-6$
   3. (c)$8$
   4. (d)$10$
   Show answer

   (d) $10$

   Step-by-step solution →
6. Q266 CBSE 2023
   The ​area of ​the triangle formed ​by the line $\frac{x}{a}+\frac{y}{b}=1$ with ​the ​coordinate axes ​is:

   1. (a)$ab$
   2. (b)$\frac{1}{2}ab$
   3. (c)$\frac{1}{4}ab$
   4. (d)$2ab$
   Show answer

   (b) $\frac{1}{2}ab$

   Step-by-step solution →
7. Q267 CBSE 2023
   Directions: A statement ​of Assertion (A) is followed by a ​statement ​of ​Reason ​(R). Choose ​the ​correct option.

   Assertion (A): Point $P(0,2)$ is the point of intersection of $y$-axis with the line $3x+2y=4$.

   Reason (R): The distance of point $P(0,2)$ from $x$-axis is $2$ units.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

   Step-by-step solution →
8. Q268 CBSE 2023
   Assertion (A): If the points $A(4,3)$ and $B(x,5)$ lie on a circle with centre $O(2,3)$, then the value of $x$ is $2$.

   Reason (R): Centre of a circle is the mid-point of each chord of the circle.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (c) Assertion (A) is true, but Reason (R) is false.

   Step-by-step solution →
9. Q269 CBSE 2023
   Find the ratio in which ​a line ​segment ​joining points $(1,-4)$ ​and $(6,5)$ is ​divided by the x-axis.
   Show answer

   The x-axis divides the segment in the ratio $4:5$.

   Step-by-step solution →
10. Q270 CBSE 2023
    Find the ​coordinates ​of the point ​which divides the ​line ​segment joining the points $(7,-1)$ ​and $(-3,4)$ internally in ​the ratio $2:3$.
    Show answer

    The point is $(3,1)$

    Step-by-step solution →
11. Q271 CBSE 2023
    The ​line ​segment joining ​the ​points $A(4,-5)$ ​and $B(4,5)$ is ​divided by the point $P$ such that $AP:AB=2:5$. Find ​the ​coordinates of $P$.
    Show answer

    $P=(4,-1)$

    Step-by-step solution →
12. Q272 CBSE 2023
    Point $P(x,y)$ is ​equidistant ​from ​points $A(5,1)$ ​and $B(1,5)$. ​Prove ​that $x=y$.
    Show answer

    $x=y$ (proved)

    Step-by-step solution →
13. Q273 CBSE 2023
    Find the ​value(s) of $y$ ​for ​which ​the distance between ​the points $A(3,-1)$ ​and $B(11,y)$ ​is $10$ units.
    Show answer

    $y=5$ or $y=-7$

    Step-by-step solution →
14. Q274 CBSE 2023
    A line intersects $y$-axis and $x$-axis at point P ​and Q, ​respectively. If $R(2,5)$ ​is ​the mid-point of line segment PQ, ​then ​find the coordinates of P and ​Q.
    Show answer

    $P=(0,10)$ and $Q=(4,0)$

    Step-by-step solution →
15. Q275 CBSE 2023
    Find the coordinates ​of ​the point ​which divides ​the ​join ​of $A(-1,7)$ and $B(4,-3)$ ​in the ​ratio $2:3$.

    Show answer

    $(1,3)$

    Step-by-step solution →
16. Q276 CBSE 2023
    If the ​points $A(2,3)$, $B(-5,6)$, $C(6,7)$ and $D(p,4)$ ​are ​the ​vertices of ​a parallelogram $ABCD$, find the value ​of $p$.

    Show answer

    $p=13$

    Step-by-step solution →
17. Q277 CBSE 2023
    Show that the ​points $(-2,3)$, $(8,3)$ and $(6,7)$ ​are the vertices ​of ​a ​right-angled ​triangle.
    Show answer

    Since $B{C}^2+C{A}^2=A{B}^2=100$, the triangle is right-angled at $C$.

    Step-by-step solution →
18. Q278 CBSE 2023
    Find the ​positive ​value of $y$ ​for which ​the distance between ​the ​points $A(3,-1)$ ​and $B(11,y)$ is $10$ ​units.
    Show answer

    $y=5$

    Step-by-step solution →
19. Q279 CBSE 2023
    If the point $P(3,-3)$ ​is ​equidistant ​from the ​points $A(4,9)$ and $B(-9,k)$, find ​the ​value(s) of $k$.
    Show answer

    $k=-2$ or $k=-4$

    Step-by-step solution →
20. Q280 CBSE 2023
    Show that the points $(-3,-3)$, $(3,3)$ ​and $(-3\sqrt{3},3\sqrt{3})$ are ​the ​vertices ​of an ​equilateral ​triangle.
    Show answer

    All sides equal $\sqrt{72}=6\sqrt{2}$, so the triangle is equilateral.

    Step-by-step solution →