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 4 of 6

1. Q61 Exemplar · Exercise 7.3
   If ​the point A $(2,-4)$ is equidistant ​from ​P $(3,8)$ ​and Q $(-10,y)$, find the values of $y$. ​Also find ​distance PQ.
   Show answer

   $y=-3$ or $y=-5$. Then $PQ=\sqrt{290}$ (for $y=-3$) or $PQ=13\sqrt{2}$ (for $y=-5$).

   Step-by-step solution →
2. Q62 Exemplar · Exercise 7.3
   Find the ​area ​of ​the ​triangle ​whose vertices are $(-8,4)$, $(-6,6)$ and $(-3,9)$.
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   The area is $0$ square units; the three points $(-8,4)$, $(-6,6)$, $(-3,9)$ are collinear.

   Step-by-step solution →
3. Q63 Exemplar · Exercise 7.3
   In what ratio does the ​x-axis divide ​the ​line segment joining the points $(-4,-6)$ and $(-1,7)$? ​Find the ​coordinates ​of the point of ​division.
   Show answer

   The x-axis divides the segment in the ratio $6:7$; the point of division is $\left(-\frac{34}{13},0\right)$.

   Step-by-step solution →
4. Q64 Exemplar · Exercise 7.3
   If $P(9a-2,-b)$ divides line segment ​joining $A(3a+1,-3)$ ​and $B(8a,5)$ in ​the ratio $3:1$, ​find the values ​of $a$ ​and $b$.
   Show answer

   $a=1$ and $b=-3$.

   Step-by-step solution →
5. Q65 Exemplar · Exercise 7.3
   If $(a,b)$ ​is the ​mid-point of ​the line segment joining the ​points $A(10,-6)$ ​and $B(k,4)$ ​and $a-2b=18$, ​find ​the value of $k$ and the distance $AB$.
   Show answer

   $k=22$ and $AB=\sqrt{244}=2\sqrt{61}\approx 15.62$ units.

   Step-by-step solution →
6. Q66 Exemplar · Exercise 7.3
   The centre of a circle ​is $(2a,a-7)$. Find the values of $a$ if the circle ​passes ​through the ​point $(11,-9)$ and ​has diameter $10\sqrt{2}$ ​units.
   Show answer

   $a=3$ or $a=5$.

   Step-by-step solution →
7. Q67 Exemplar · Exercise 7.3
   The line segment ​joining the points A(3, 2) and B(5, ​1) is divided ​at the point P in the ​ratio 1:2 and it lies on the line $3x-18y+k=0$. Find ​the ​value ​of k.
   Show answer

   $P=\left(\frac{11}{3},\frac{5}{3}\right)$ and substituting into the line gives $k=19$.

   Step-by-step solution →
8. Q68 Exemplar · Exercise 7.3
   If $D\left(\frac{-1}{2},\frac{5}{2}\right)$, $E(7,3)$ ​and $F\left(\frac{7}{2},\frac{7}{2}\right)$ are the ​midpoints of ​sides of $△ABC$, find ​the area ​of the $△ABC$.
   Show answer

   Area of $△ABC=11$ square units.

   Step-by-step solution →
9. Q69 Exemplar · Exercise 7.3
   The ​points $A(2,9)$, $B(a,5)$ and $C(5,5)$ ​are the vertices of a triangle $ABC$ ​right angled at $B$. Find ​the values of $a$ ​and hence the ​area of $△ABC$.
   Show answer

   a = 2 only; Area = 6 square units

   Step-by-step solution →
10. Q70 Exemplar · Exercise 7.3
    Find the coordinates of ​the ​point $R$ on the ​line segment joining the ​points $P(-1,3)$ ​and $Q(2,5)$ ​such that $PR=\frac{3}{5}PQ$.
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    $R=\left(\frac{4}{5},\frac{21}{5}\right)$.

    Step-by-step solution →
11. Q71 Exemplar · Exercise 7.3
    Find ​the values ​of $k$ ​if ​the ​points $A(k+1,2k)$, $B(3k,2k+3)$ and $C(5k-1,5k)$ ​are collinear.
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    $k=\frac{1}{2}$ or $k=2$.

    Step-by-step solution →
12. Q72 Exemplar · Exercise 7.3
    Find ​the ratio ​in ​which the line $2x+3y-5=0$ divides the line segment ​joining the points $(8,-9)$ and $(2,1)$. Also find the coordinates ​of ​the point of ​division.
    Show answer

    The line divides the segment in the ratio $8:1$, and the point of division is $\left(\frac{8}{3},-\frac{1}{9}\right)$.

    Step-by-step solution →
13. Q73 CBSE 2026
    The line segment ​joining the ​points $P(-4,-2)$ and $Q(10,4)$ is divided ​by the ​y-axis in ​the ratio :

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

    (a) $2:5$

    Step-by-step solution →
14. Q74 CBSE 2026
    The distance ​between the ​points $(-2,5)$ and $(5,-2)$ ​is

    1. (a)$7\sqrt{2}$
    2. (b)$14$
    3. (c)$2\sqrt{7}$
    4. (d)$7$
    Show answer

    (a) $7\sqrt{2}$

    Step-by-step solution →
15. Q75 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 →
16. Q76 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 →
17. Q77 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 →
18. Q78 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 →
19. Q79 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 →
20. Q80 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 →