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 11 of 22

1. Q201 CBSE 2024
   If the distance ​between the ​points $(3,-5)$ ​and $(x,-5)$ ​is $15$ units, then ​the values ​of $x$ ​are :

   1. (a)$12,-18$
   2. (b)$-12,18$
   3. (c)$18,5$
   4. (d)$-9,-12$
   Show answer

   (b) $-12,18$

   Step-by-step solution →
2. Q202 CBSE 2024
   $XOYZ$ ​is ​a rectangle ​with vertices $X(-3,0)$, $O(0,0)$, $Y(0,4)$ and $Z(x,y)$. ​The ​length ​of its each ​diagonal is

   1. (a)$5$ units
   2. (b)$\sqrt{5}$ units
   3. (c)$x^2+y^2$ units
   4. (d)$4$ units
   Show answer

   (a) $5$ units

   Step-by-step solution →
3. Q203 CBSE 2024
   The point ​on x-axis which ​is ​equidistant from the ​points $(5,-3)$ ​and $(4,2)$ ​is ​:

   1. (a)$(4.5,0)$
   2. (b)$(7,0)$
   3. (c)$(0.5,0)$
   4. (d)$(-7,0)$
   Show answer

   (b) $(7,0)$

   Step-by-step solution →
4. Q204 CBSE 2024
   The ​mid-point of the ​line ​segment ​AB joining $A(-2,8)$ and $B(-6,4)$ ​is ​:

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

   (c) (-4, 6)

   Step-by-step solution →
5. Q205 CBSE 2024
   The diameter of a ​circle is ​of length $6$ cm. ​If one ​end ​of ​the diameter is $(-4,0)$, the other end on x-axis is ​at:

   1. (a)$(0,2)$
   2. (b)$(6,0)$
   3. (c)$(2,0)$
   4. (d)$(4,0)$
   Show answer

   (c) $(2,0)$

   Step-by-step solution →
6. Q206 CBSE 2024
   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 →
7. Q207 CBSE 2024
   The ​centre ​of a circle is ​at $(2,0)$. ​If one end of ​a diameter is at $(6,0)$, ​then the other end is at ​:

   1. (a)$(0,0)$
   2. (b)$(4,0)$
   3. (c)$(-2,0)$
   4. (d)$(-6,0)$
   Show answer

   (c) $(-2,0)$

   Step-by-step solution →
8. Q208 CBSE 2024
   The ​points $(-2,-2)$, $(6,-2)$ and $(2,1)$ ​are ​the ​vertices of:

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

   (b) an isosceles triangle

   Step-by-step solution →
9. Q209 CBSE 2024
   Assertion (A): Mid-point of a line segment divides the line segment in the ratio $1:1$.

   Reason (R): The ratio in which the point $(-3,k)$ divides the line segment joining the points $(-5,4)$ and $(-2,3)$ is $1:2$.

   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 →
10. Q210 CBSE 2024
    Assertion (A): The distance of the point $(-3,5)$ from the x-axis is $3$ units.

    Reason (R): Abscissa of a point gives the distance of the point from the y-axis.

    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

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

    Step-by-step solution →
11. Q211 CBSE 2024
    Assertion (A): The point which divides the line segment joining the points $A(1,2)$ and $B(-1,1)$ internally in the ratio $1:2$ is $\left(\frac{-1}{3},\frac{5}{3}\right)$.

    Reason (R): The coordinates of the point which divides the line segment joining the points $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m_1:m_2$ are $\left(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\right)$.

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

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

    Step-by-step solution →
12. Q212 CBSE 2024
    Directions: A ​statement of Assertion (A) ​is followed by ​a statement of Reason (R). ​Choose the ​correct ​option.

    Assertion (A): The distance of $P(a,b)$ from origin is $a^2+b^2$.

    Reason (R): The distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

    1. (a)Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true. 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

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

    Step-by-step solution →
13. Q213 CBSE 2024
    Directions: A statement ​of ​Assertion ​(A) is followed by a statement of ​Reason (R). Choose ​the ​correct option.

    Assertion (A): The point $(0,4)$ lies on $y$-axis.

    Reason (R): The $x$-coordinate of a point, lying on $y$-axis, is zero.

    1. (a)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are correct 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

    (a) Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
14. Q214 CBSE 2024
    If $Q(0,2)$ is ​equidistant ​from $P(5,-3)$ ​and $R(x,7)$, find ​the value(s) ​of $x$.
    Show answer

    $x=5$ or $x=-5$, so $R$ is $(5,7)$ or $(-5,7)$.

    Step-by-step solution →
15. Q215 CBSE 2024
    If $A(1,1)$ and $B(7,9)$ are ​the end points of a ​diameter ​of a circle, then ​find the ​co-ordinates of ​the centre of ​the circle.
    Show answer

    The centre of the circle is $(4,5)$.

    Step-by-step solution →
16. Q216 CBSE 2024
    Find ​the ​type ​of triangle $ABC$ formed ​whose ​vertices are $A(1,0)$, $B(-5,0)$ ​and $C(-2,5)$.
    Show answer

    $△ABC$ is an isosceles triangle: $CA=CB=\sqrt{34}$ units and $AB=6$ units. It is not right-angled, since $A{B}^2=36<B{C}^2+C{A}^2=68$; all its angles are acute.

    Step-by-step solution →
17. Q217 CBSE 2024
    Find the ratio in ​which ​the point $(3,y)$ ​divides the ​line segment joining the points $(-2,-5)$ ​and $(6,3)$. ​Also, find the value ​of $y$.
    Show answer

    The point $(3,y)$ divides the segment in the ratio $5:3$ (internally), and $y=0$.

    Step-by-step solution →
18. Q218 CBSE 2024
    Find ​a point on $y$-axis ​which is equidistant ​from the ​points $A(6,5)$ ​and $B(-4,3)$.
    Show answer

    The required point is $(0,9)$.

    Step-by-step solution →
19. Q219 CBSE 2024
    Find a ​relation ​between $x$ and y such that the ​point $P(x,y)$ is equidistant ​from the points $A(7,1)$ and $B(3,5)$.
    Show answer

    The required relation is $x-y-2=0$, that is, $x=y+2$.

    Step-by-step solution →
20. Q220 CBSE 2024
    Points $A(-1,y)$ and $B(5,7)$ lie ​on a circle with ​centre $O(2,-3y)$ ​such that ​AB is a diameter ​of the circle. ​Find the value of ​y. Also, find the ​radius of the circle.
    Show answer

    $y=-1$, and the radius of the circle is $5$ units.

    Step-by-step solution →