Class 10 Maths · Chapter 7

Coordinate Geometry

118 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 5 of 6

1. Q81 CBSE 2026
   The fourth vertex $D$ of ​a parallelogram $ABCD$ ​whose ​three ​vertices are $A(-4,1)$, $B(4,5)$ ​and $C(6,1)$ ​is:

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

   (a) $(-2,-3)$

   Step-by-step solution →
2. Q82 CBSE 2026
   In the given ​figure, the length of ​hypotenuse ​of the ​right $△AOB$ ​is ​:

   1. (a)$3$ units
   2. (b)$4$ units
   3. (c)$5$ units
   4. (d)$25$ units
   Show answer

   (c) $5$ units

   Step-by-step solution →
3. Q83 CBSE 2026
   The ​co-ordinates of the mid-point ​of ​the line segment joining points $A(p-1,q+1)$ ​and $B(p+1,q-1)$ ​are given ​by ​:

   1. (a)$(p,q)$
   2. (b)$(2p,2q)$
   3. (c)$\left(\frac{p+1}{2},\frac{q+1}{2}\right)$
   4. (d)$\left(\frac{p-1}{2},\frac{q-1}{2}\right)$
   Show answer

   (a) $(p,q)$

   Step-by-step solution →
4. Q84 CBSE 2026
   The ratio ​in ​which ​the $x$-axis ​divides ​the ​line segment joining the points $A(-8,4)$ and $B(-6,-2)$ ​is:

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

   (c) $2:1$

   Step-by-step solution →
5. Q85 CBSE 2026
   In ​the given ​figure, a ​circle is centred ​at $(1,2)$. The diameter ​of the circle is

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

   (d) $2\sqrt{5}$

   Step-by-step solution →
6. Q86 CBSE 2026
   The ​distance between ​points $(3,0)$ ​and $(0,-3)$ is ​:

   1. (a)$3$ units
   2. (b)$6$ units
   3. (c)$\sqrt{6}$ units
   4. (d)$\sqrt{18}$ units
   Show answer

   (d) $\sqrt{18}$ units

   Step-by-step solution →
7. Q87 CBSE 2026
   The mid-point ​of the ​line ​segment joining ​the ​points $(5,-4)$ and $(6,4)$ lies on ​:

   1. (a)$x$-axis
   2. (b)$y$-axis
   3. (c)origin
   4. (d)neither $x$-axis nor $y$-axis
   Show answer

   (a) $x$-axis

   Step-by-step solution →
8. Q88 CBSE 2026
   The distance ​of the ​point $A(4a,3a)$ from ​the ​x-axis ​is ​:

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

   (a) $3a$

   Step-by-step solution →
9. Q89 CBSE 2026
   The ​distance ​between ​the points $(-4,2)$ ​and $(1,0)$ ​is :

   1. (a)$\sqrt{13}$ units
   2. (b)$3$ units
   3. (c)$9$ units
   4. (d)$\sqrt{29}$ units
   Show answer

   (d) $\sqrt{29}$ units

   Step-by-step solution →
10. Q90 CBSE 2026
    The ​distance ​between the ​points $(a\cos \theta +b\sin \theta ,0)$ ​and $(0,a\sin \theta -b\cos \theta )$ ​is

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

    (a) $\sqrt{a^2+b^2}$

    Step-by-step solution →
11. Q91 CBSE 2026
    In ​the ​given figure, $△ABC$ is an equilateral triangle. $AD$ is a ​median ​of ​the triangle ​joining the points $A\left(0,\frac{5\sqrt{3}}{2}\right)$, $D(0,0)$. ​Points $B$ and $C$ are (in same order) :

    1. (a)$(-5,0),(5,0)$
    2. (b)$\left(-\frac{5}{2},0\right),\left(\frac{5}{2},0\right)$
    3. (c)$(-10,0),(10,0)$
    4. (d)$(-5\sqrt{3},0),(5\sqrt{3},0)$
    Show answer

    (b) $\left(-\frac{5}{2},0\right),\left(\frac{5}{2},0\right)$

    Step-by-step solution →
12. Q92 CBSE 2026
    Find ​the coordinates ​of ​the point which ​divides the ​line segment joining ​the points $A(-6,10)$ ​and $B(3,-8)$ ​in the ratio $2:7$.
    Show answer

    The required point is $(-4,6)$.

    Step-by-step solution →
13. Q93 CBSE 2026
    An ant started moving ​from the point $A(2,3)$ and ​moved along the ​line segment $AB$. It covered three-fourth of the distance $AB$ and reached ​at a ​point $C(x,y)$. If ​the coordinates ​of the point $B$ are $(10,15)$, find the coordinates of the point $C$.
    Show answer

    The coordinates of the point $C$ are $(8,12)$.

    Step-by-step solution →
14. Q94 CBSE 2026
    The ​point $P(x,y)$ lies on a semi-circular arc having diameter $AB$ as shown ​in the given figure. The coordinates of points $A$ and $B$ are $(3,0)$ and $(0,4)$ ​respectively. ​Find ​the ​relation between $x$ ​and $y$, if $P{A}^2+P{B}^2=A{B}^2$.

    Show answer

    The required relation is $x^2+y^2-3x-4y=0$

    Step-by-step solution →
15. Q95 CBSE 2026
    Vertices ​of a right ​triangle $ABC$ with $\angle B=90^{\circ }$ ​are $A(3,4)$, $B(1,1)$ and $C(-8,7)$. Find ​the ​value ​of $\tan A$.
    Show answer

    $\tan A=3$.

    Step-by-step solution →
16. Q96 CBSE 2026
    Using distance ​formula, ​prove that the ​points $A(2,3)$, $B(-7,0)$ ​and $C(-1,2)$ ​are ​collinear.
    Show answer

    The distances are $AB=3\sqrt{10}$, $BC=2\sqrt{10}$ and $CA=\sqrt{10}$. Since $CA+CB=\sqrt{10}+2\sqrt{10}=3\sqrt{10}=AB$, the point $C$ lies on segment $AB$, so $A$, $B$ and $C$ are collinear.

    Step-by-step solution →
17. Q97 CBSE 2026
    The coordinates of ​the centre ​of a circle ​are $(x-7,2x)$. Find the value(s) of '$x$', if the circle ​passes through ​the ​point $(-9,11)$ and ​has radius $5\sqrt{2}$ units.
    Show answer

    The values are $x=3$ or $x=5$.

    Step-by-step solution →
18. Q98 CBSE 2026
    If the ​points $A(4,5)$, $B(m,6)$, $C(4,3)$ and $D(1,n)$ ​taken in ​this order ​are the ​vertices of a parallelogram $ABCD$, then find ​the ​values ​of $m$ and $n$.
    Show answer

    $m=7$ and $n=2$.

    Step-by-step solution →
19. Q99 CBSE 2026
    If $A(a,0)$, $B(1,1)$ ​and $C(0,b)$ ​form ​a triangle, right angled at $B$ when joined, then ​establish a relation ​between $a$ ​and $b$.
    Show answer

    The required relation is $a+b=2$.

    Step-by-step solution →
20. Q100 CBSE 2026
    A $(-2,3)$ and B $(4,1)$ are end ​points of the ​diameter of a ​semi-circle. ​The semi-circle intersects the $y$-axis at point P. Find ​the co-ordinates ​of ​the point ​P.
    Show answer

    $P=(0,5)$ or $P=(0,-1)$ — the two points where the circle on diameter $AB$ meets the $y$-axis.

    Step-by-step solution →