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 8 of 22

1. Q141 CBSE 2025
   The ​point ​on $y$-axis ​equidistant from ​the points $A(1,3)$ ​and $B(4,4)$ is

   1. (a)$(0,11)$
   2. (b)$(11,0)$
   3. (c)$(0,13)$
   4. (d)$(0,12)$
   Show answer

   (a) $(0,11)$

   Step-by-step solution →
2. Q142 CBSE 2025
   The ​point $(x,0)$ ​divides the ​line ​segment joining the points $(-4,5)$ and $(0,-10)$ ​in ​the ​ratio

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

   (d) $1:2$

   Step-by-step solution →
3. Q143 CBSE 2025
   M ​is a point on y-axis at a distance ​of 4 units ​from x-axis and it lies below the x-axis. ​The distance of point ​M from ​point Q(5, 1) is :

   1. (a)$\sqrt{2}$ units
   2. (b)$\sqrt{34}$ units
   3. (c)$\sqrt{50}$ units
   4. (d)$\sqrt{90}$ units
   Show answer

   (c) $\sqrt{50}$ units

   Step-by-step solution →
4. Q144 CBSE 2025
   The ​points $(-4,0)$, $(4,0)$ and $(0,-3)$ ​are ​the ​vertices ​of ​a/an:

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

   (b) isosceles triangle

   Step-by-step solution →
5. Q145 CBSE 2025
   The distance ​of ​point $P(3,4)$ ​from the $x$-axis ​is

   1. (a)$3$ units
   2. (b)$4$ units
   3. (c)$5$ units
   4. (d)$7$ units
   Show answer

   (b) $4$ units

   Step-by-step solution →
6. Q146 CBSE 2025
   If the points $A(5,4)$ and $B(x,6)$ are ​on ​a ​circle with centre $(3,4)$, ​then ​the value ​of $x$ ​is:

   1. (a)$6$
   2. (b)$7$
   3. (c)$3$
   4. (d)$1$
   Show answer

   (c) $3$

   Step-by-step solution →
7. Q147 CBSE 2025
   The ratio in which the ​line segment ​joining the points $A(-4,8)$ and $B(5,-10)$ ​is divided by ​the ​point $P(-2,4)$ ​is

   1. (a)$1:3$
   2. (b)$3:4$
   3. (c)$2:7$
   4. (d)$2:5$
   Show answer

   (c) $2:7$

   Step-by-step solution →
8. Q148 CBSE 2025
   The ​coordinates ​of the ​point ​where the ​line $\frac{x}{a}+\frac{y}{b}=5$ intersects y-axis ​are

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

   (d) $(0,5b)$

   Step-by-step solution →
9. Q149 CBSE 2025
   The line ​represented ​by the ​equation $x-y=0$ ​is :

   1. (a)parallel to x-axis
   2. (b)parallel to y-axis
   3. (c)passing through the origin
   4. (d)passing through the point $(3,2)$
   Show answer

   (c) passing through the origin

   Step-by-step solution →
10. Q150 CBSE 2025
    $A(-4,5)$ and $C(8,2)$ ​are the two opposite vertices of ​a parallelogram $ABCD$. ​Its diagonals intersect ​each other at $P(a,b)$. The relation between $a$ and $b$ ​is ​:

    1. (a)$b=a-1.5$
    2. (b)$b=a+1.5$
    3. (c)$b=a-4.5$
    4. (d)$b=a+4.5$
    Show answer

    (b) $b=a+1.5$

    Step-by-step solution →
11. Q151 CBSE 2025
    $AOBC$ is a rectangle whose three vertices are $A(0,2)$, $O(0,0)$ ​and $B(4,0)$. The square ​of the length of ​its diagonal ​is ​equal to :

    1. (a)$36$
    2. (b)$20$
    3. (c)$16$
    4. (d)$4$
    Show answer

    (b) $20$

    Step-by-step solution →
12. Q152 CBSE 2025
    Read the ​Assertion (A) and ​Reason ​(R) ​carefully and choose ​the correct ​option.

    Assertion (A): The point $(-2,4)$ divides the line segment joining the points $(-4,8)$ and $(5,-10)$ in the ratio $2:7$ internally.

    Reason (R): If three points $P$, $Q$ and $R$ are collinear, then $PQ+QR=PR$.

    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

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

    Step-by-step solution →
13. Q153 CBSE 2025
    Directions: In ​the ​following question, a ​statement of Assertion (A) is followed by a statement of Reason ​(R). Choose ​the ​correct ​option.

    Assertion (A): If the distance between the points $A(2,-2)$ and $B(10,y)$ is $10$, then the value of $y$ is $4$.

    Reason (R): Distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

    1. (a)Both Assertion (A) and Reason (R) are true 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

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

    Step-by-step solution →
14. Q154 CBSE 2025
    The coordinates of the end points ​of the line segment $AB$ ​are $A(-2,-2)$ ​and $B(2,-4)$. $P$ is the ​point on $AB$ ​such that $BP=\frac{4}{7}AB$. Find the coordinates ​of ​point $P$.
    Show answer

    The coordinates of $P$ are $\left(-\frac{2}{7},-\frac{20}{7}\right)$, since $P$ divides $AB$ in the ratio $3:4$.

    Step-by-step solution →
15. Q155 CBSE 2025
    Point $P(x,0)$ divides the line ​segment joining the points $(2,8)$ and $(-3,-5)$ ​in ​a certain ratio. ​Find the ratio and ​hence ​find ​the value of $x$.
    Show answer

    The ratio is $8:5$ and $x=-\frac{14}{13}$.

    Step-by-step solution →
16. Q156 CBSE 2025
    Prove that abscissa ​of a point $P$ ​which is ​equidistant from ​points with ​coordinates $A(7,1)$ and $B(3,5)$ is $2$ more than its ​ordinate.
    Show answer

    For $P(x,y)$, $P{A}^2=P{B}^2$ simplifies to $x=y+2$, so the abscissa of $P$ is $2$ more than its ordinate. Hence proved.

    Step-by-step solution →
17. Q157 CBSE 2025
    The coordinates ​of the ​centre of a circle are $(2a,a-7)$. Find the value(s) of $a$ if the ​circle passes through the point $(11,-9)$ ​and ​has diameter $10\sqrt{2}$ units.
    Show answer

    The value of $a$ is $3$ or $5$, giving the centre $(6,-4)$ or $(10,-2)$.

    Step-by-step solution →
18. Q158 CBSE 2025
    Find ​the coordinates of ​the points ​of trisection of line ​segment joining ​the ​points $(-4,1)$ ​and $(6,5)$.
    Show answer

    The points of trisection are $\left(-\frac{2}{3},\frac{7}{3}\right)$, nearer to $(-4,1)$, and $\left(\frac{8}{3},\frac{11}{3}\right)$, nearer to $(6,5)$.

    Step-by-step solution →
19. Q159 CBSE 2025
    Find the coordinates of the ​point ​C which lies on ​the line AB produced such that $AC=2BC$, ​where coordinates ​of points ​A and B are $(-1,7)$ and $(4,-3)$ respectively.
    Show answer

    The coordinates of $C$ are $(9,-13)$.

    Step-by-step solution →
20. Q160 CBSE 2025
    Find the ​coordinates ​of the ​point which ​divides ​the join of $(-1,7)$ and $(4,-3)$ in the ​ratio $2:3$.
    Show answer

    The required point is $(1,3)$.

    Step-by-step solution →