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 1 of 6

1. Q1 NCERT · Exercise 7.1
   Find ​the distance between the ​following ​pairs of ​points:

   1. (i)(2,3), ​(4,1)
   2. (ii)(-5,7), (-1,3)
   3. (iii)(a,b), (-a,-b).
   Show answer

   (i) $2\sqrt{2}$; (ii) $4\sqrt{2}$; (iii) $2\sqrt{a^2+b^2}$.

   Step-by-step solution →
2. Q2 NCERT · Exercise 7.1
   Find the distance between ​the points $(0,0)$ and $(36,15)$. Can you ​now find the distance between the ​two ​towns A and ​B discussed ​in Section 7.2?
   Show answer

   Distance $=39$ units, so towns A and B are $39$ km apart.

   Step-by-step solution →
3. Q3 NCERT · Exercise 7.1
   Determine ​if ​the points (1, ​5), (2, ​3) and ​(-2, ​-11) are collinear.
   Show answer

   The points are **not** collinear (area of $△ABC=11\ne 0$).

   Step-by-step solution →
4. Q4 NCERT · Exercise 7.1
   Check whether (5, -2), (6, ​4) and (7, ​-2) are ​the ​vertices ​of an isosceles triangle.
   Show answer

   Yes — the points form an isosceles triangle with $AB=BC=\sqrt{37}$ and $CA=2$.

   Step-by-step solution →
5. Q5 NCERT · Exercise 7.1
   In ​a classroom, 4 friends are seated at ​the points A, ​B, C and D ​as shown in Fig. 7.8. Champa and Chameli walk into ​the ​class and after observing ​for a few ​minutes Champa asks Chameli, 'Don't you think ABCD is a square?' Chameli disagrees. Using distance formula, find which of them is correct.

   Show answer

   All four sides equal $\sqrt{18}$ and both diagonals equal $6$, so $ABCD$ is a square. Champa is correct.

   Step-by-step solution →
6. Q6 NCERT · Exercise 7.1
   Name the ​type of ​quadrilateral formed, if any, by ​the following points, and ​give reasons for your ​answer: ​

   1. (i)$(-1,-2),(1,0),(-1,2),(-3,0)$; ​
   2. (ii)$(-3,5),(3,1),(0,3),(-1,-4)$;
   3. (iii)$(4,5),(7,6),(4,3),(1,2)$.
   Show answer

   (i) Square; (ii) No quadrilateral (three points are collinear); (iii) Parallelogram.

   Step-by-step solution →
7. Q7 NCERT · Exercise 7.1
   Find the ​point ​on the $x$-axis ​which is ​equidistant from $(2,-5)$ ​and $(-2,9)$.
   Show answer

   The required point is $(-7,0)$.

   Step-by-step solution →
8. Q8 NCERT · Exercise 7.1
   Find the values ​of $y$ ​for ​which the ​distance ​between the points $P(2,-3)$ ​and $Q(10,y)$ is $10$ ​units.
   Show answer

   $y=3$ or $y=-9$.

   Step-by-step solution →
9. Q9 NCERT · Exercise 7.1
   If $Q(0,1)$ is ​equidistant from $P(5,-3)$ and $R(x,6)$, ​find ​the values of $x$. Also find ​the ​distances QR ​and PR.
   Show answer

   $x=4$ or $x=-4$; $QR=\sqrt{41}$; $PR=\sqrt{82}$ (for $x=4$) or $9\sqrt{2}$ (for $x=-4$).

   Step-by-step solution →
10. Q10 NCERT · Exercise 7.1
    Find ​a relation between $x$ ​and $y$ such ​that ​the point $(x,y)$ is equidistant ​from ​the point $(3,6)$ ​and $(-3,4)$.
    Show answer

    The required relation is $3x+y=5$ (equivalently $3x+y-5=0$).

    Step-by-step solution →
11. Q11 NCERT · Exercise 7.2
    Find the coordinates of the ​point which ​divides ​the join ​of $(-1,7)$ ​and $(4,-3)$ in the ​ratio $2:3$.
    Show answer

    $P=(1,3)$

    Step-by-step solution →
12. Q12 NCERT · Exercise 7.2
    Find the coordinates ​of ​the ​points of ​trisection of the ​line segment ​joining (4, -1) and (-2, -3).
    Show answer

    Trisection points: $P=\left(2,-\frac{5}{3}\right)$ and $Q=\left(0,-\frac{7}{3}\right)$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 7.2
    To conduct ​Sports Day activities, in your rectangular shaped ​school ground ABCD, lines have ​been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as ​shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth ​line ​and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line ​segment joining the two ​flags, where should she post her flag?

    Show answer

    Distance between green and red flags $=\sqrt{61}\approx 7.81$ m; blue flag at $(5,22.5)$ — on the 5th line, $22.5$ m from $A$.

    Step-by-step solution →
14. Q14 NCERT · Exercise 7.2
    Find ​the ratio ​in ​which the line segment joining ​the points $(-3,10)$ ​and $(6,-8)$ is ​divided by $(-1,6)$.
    Show answer

    Ratio $=2:7$ (internal division).

    Step-by-step solution →
15. Q15 NCERT · Exercise 7.2
    Find ​the ​ratio in ​which the line ​segment joining $A(1,-5)$ and $B(-4,5)$ is divided by the $x$-axis. Also find the coordinates of the point of ​division.
    Show answer

    Ratio $=1:1$; point of division $P=\left(-\frac{3}{2},0\right)$.

    Step-by-step solution →
16. Q16 NCERT · Exercise 7.2
    If $(1,2),(4,y),(x,6)$ and $(3,5)$ are ​the ​vertices ​of a ​parallelogram taken ​in order, ​find $x$ ​and $y$.
    Show answer

    $x=6$ and $y=3$.

    Step-by-step solution →
17. Q17 NCERT · Exercise 7.2
    Find ​the coordinates of ​a point $A$, where $AB$ is ​the diameter of ​a circle ​whose centre is $(2,-3)$ and $B$ is $(1,4)$.
    Show answer

    $A=(3,-10)$.

    Step-by-step solution →
18. Q18 NCERT · Exercise 7.2
    If $A$ ​and $B$ are $(-2,-2)$ and $(2,-4)$ respectively, find the ​coordinates ​of $P$ such that $AP=\frac{3}{7}AB$ and $P$ lies on the line segment $AB$.
    Show answer

    $P=\left(-\frac{2}{7},-\frac{20}{7}\right)$.

    Step-by-step solution →
19. Q19 NCERT · Exercise 7.2
    Find ​the coordinates ​of ​the points which divide the line segment joining A(-2, ​2) and ​B(2, 8) into four ​equal parts.
    Show answer

    $P_1=\left(-1,\frac{7}{2}\right),P_2=(0,5),P_3=\left(1,\frac{13}{2}\right)$.

    Step-by-step solution →
20. Q20 NCERT · Exercise 7.2
    Find ​the area ​of ​a rhombus ​if its ​vertices are ​(3, 0), (4, 5), ​(-1, 4) and (-2, -1) taken in order. [Hint: ​Area of a rhombus = $\frac{1}{2}$ (product of its diagonals)]
    Show answer

    Area $=24$ square units.

    Step-by-step solution →