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 13 of 22

1. Q241 CBSE 2024
   Resident Welfare Association (RWA) of Gulmohar Society in Delhi, ​have installed three electric poles A, B and C in the society's ​common park. Despite these three poles, ​some parts of the park are ​still ​in the dark. So, RWA decides to have one more electric pole D in the park. The park can be modelled as a ​coordinate ​system given below, where the poles are at A(2, 7), B(6, 6) and C(5, 4). On the basis of ​the above information, answer the following questions.

   1. (i)What is the position of the pole C?[1]
   2. (ii)What is the distance of the pole B from the corner O of the park?[1]
   3. (iii)(a)Find the position of the fourth pole D so that the four points A, B, C and D form a parallelogram ABCD.[2]
   4. (iii)(b)Find the distance between poles A and C.[2]
   Show answer

   (i) Pole C is at $(5,4)$; (ii) $OB=6\sqrt{2}$ units $\approx 8.49$ units; (iii)(a) $D$ is at $(1,5)$; (iii)(b) $AC=3\sqrt{2}$ units $\approx 4.24$ units.

   Step-by-step solution →
2. Q242 CBSE 2024
   (Continuation of the electric-poles case study.) ​On ​the ​basis of ​the information about poles A(2, 7), B(6, 6) and C(5, 4) in the park modelled as a coordinate system, ​answer the ​following ​questions.

   1. (i)What is the position of the pole C?[1]
   2. (ii)What is the distance of the pole B from the corner O of the park?[1]
   3. (iii)(a)Find the position of the fourth pole D so that the four points A, B, C and D form a parallelogram ABCD.[2]
   4. (iii)(b)Find the distance between poles A and C.[2]
   Show answer

   (i) Pole C is at $(5,4)$; (ii) $OB=6\sqrt{2}$ units $\approx 8.49$ units; (iii)(a) $D=(1,5)$; (iii)(b) $AC=3\sqrt{2}$ units $\approx 4.24$ units. (Part (iii) is an internal choice: attempt either (a) or (b).)

   Step-by-step solution →
3. Q243 CBSE 2024
   Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of ​the city from where bank, ​hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as $A(9,5)$, hospital as $B(-3,-1)$ and supermarket as $C(5,-5)$. A, B, C form a triangle. ​Based on ​the above information, answer the following questions :

   1. (i)Find the distance between the bank and the hospital.
   2. (ii)In between the bank and ​the supermarket, there is ​a post office plotted at E which ​is their mid-point. Find the coordinates of E. (iii)(a) In between the hospital and the supermarket, there is ​a bus stop plotted as D, which is their mid-point. If Partha wants to reach the bus stop from the bank, then how much distance does he need to cover? OR (iii)(b) P and Q are two different garment shops lying between the bank and the hospital, such that $BP=PQ=QA$. If the coordinates of P and Q are $(1,a)$ and $(b,3)$ respectively, then find the values of 'a' and 'b'.

   1. (i)Find the distance between the bank and the hospital.[1]
   2. (ii)Find the coordinates of E, the mid-point of the bank and the supermarket.[1]
   3. (iii)(a)Bus stop D is the mid-point of the hospital and supermarket; find the distance from the bank to D.[2]
   4. (iii)(b)OR With BP = PQ = QA on segment BA, P=(1,a), Q=(b,3); find a and b.[2]
   Show answer

   (i) $AB=6\sqrt{5}$ units; (ii) $E=(7,0)$; (iii)(a) $AD=8\sqrt{2}$ units; (iii)(b) $a=1$, $b=5$.

   Step-by-step solution →
4. Q244 CBSE 2024
   The top of ​a table is ​hexagonal in shape. On the basis of the coordinate ​diagram given ​(an octagonal arrangement of ​labelled ​points on a ​grid), ​answer the following questions.

   1. (i)Write the coordinates of $A$ and $B$.[1]
   2. (ii)Write the coordinates of the mid-point of the line segment joining $C$ and $D$.[1]
   3. (iii)(a)Find the distance between $M$ and $Q$.[2]
   4. (iii)(b)Find the coordinates of the point which divides the line segment joining $M$ and $N$ in the ratio $1:3$ internally.[2]
   Show answer

   (i) $A(1,9)$ and $B(5,13)$; (ii) $(11,11)$; (iii)(a) $MQ=4\sqrt{5}$ units; (iii)(b) $(6,11)$.

   Step-by-step solution →
5. Q245 CBSE 2023
   The distance ​of ​the point $(4,7)$ ​from the x-axis is ​:

   1. (a)7 units
   2. (b)5 units
   3. (c)4 units
   4. (d)10 units
   Show answer

   (a) 7 units

   Step-by-step solution →
6. Q246 CBSE 2023
   In what ratio ​does x-axis divide ​the ​line ​segment ​joining ​the points $A(2,-3)$ and $B(5,6)$ ?

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

   (d) $1:2$

   Step-by-step solution →
7. Q247 CBSE 2023
   The distance ​of ​the ​point $(5,0)$ ​from ​the ​origin ​is

   1. (a)$0$
   2. (b)$5$
   3. (c)$\sqrt{5}$
   4. (d)$5^2$
   Show answer

   (b) $5$

   Step-by-step solution →
8. Q248 CBSE 2023
   The ​distance ​of ​the ​point $(-6,8)$ from $x$-axis is

   1. (a)6 units
   2. (b)-6 units
   3. (c)8 units
   4. (d)10 units
   Show answer

   (c) 8 units

   Step-by-step solution →
9. Q249 CBSE 2023
   The ​distance of the ​point $(-1,7)$ from ​x-axis ​is :

   1. (a)$-1$
   2. (b)$7$
   3. (c)$6$
   4. (d)$\sqrt{50}$
   Show answer

   (b) $7$

   Step-by-step solution →
10. Q250 CBSE 2023
    The distance ​between ​the ​points $A(0,6)$ ​and $B(-6,2)$ is :

    1. (a)$6$ units
    2. (b)$2\sqrt{6}$ units
    3. (c)$2\sqrt{13}$ units
    4. (d)$13\sqrt{2}$ units
    Show answer

    (c) $2\sqrt{13}$ units

    Step-by-step solution →
11. Q251 CBSE 2023
    In what ​ratio, ​does $x$-axis ​divide the ​line segment ​joining ​the points $A(3,6)$ and $B(-12,-3)$ ?

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

    (d) $2:1$

    Step-by-step solution →
12. Q252 CBSE 2023
    The coordinates ​of the ​vertex $A$ ​of ​a rectangle $ABCD$ whose ​three ​vertices are given as $B(0,0)$, $C(3,0)$ ​and $D(0,4)$ are:

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

    (c) $(3,4)$

    Step-by-step solution →
13. Q253 CBSE 2023
    The ​distance ​between ​the points $(3,0)$ and $(0,-3)$ ​is

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

    (d) $3\sqrt{2}$ units

    Step-by-step solution →
14. Q254 CBSE 2023
    The point P on ​y-axis ​equidistant ​from ​the points $(-2,7)$ and $(3,6)$ is :

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

    (c) $(0,4)$

    Step-by-step solution →
15. Q255 CBSE 2023
    The ​distance of ​the ​point $(3,-5)$ from $x$-axis ​is ​:

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

    (d) 5

    Step-by-step solution →
16. Q256 CBSE 2023
    The coordinates of ​the point A, ​where AB is ​the diameter of ​the circle ​whose centre is $(3,-2)$ and ​B$(7,4)$ is :

    1. (a)$(-1,-8)$
    2. (b)$(-1,8)$
    3. (c)$(1,8)$
    4. (d)$(1,-8)$
    Show answer

    (a) $(-1,-8)$

    Step-by-step solution →
17. Q257 CBSE 2023
    The ratio ​in ​which ​the x-axis divides the ​line ​segment joining the points $A(-6,5)$ and $B(-4,-1)$ is ​:

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

    (c) $5:1$

    Step-by-step solution →
18. Q258 CBSE 2023
    The ​distance ​between ​the ​points $P\left(-\frac{11}{3},5\right)$ ​and $Q\left(-\frac{2}{3},5\right)$ ​is :

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

    (d) 3 units

    Step-by-step solution →
19. Q259 CBSE 2023
    If $(-3,a)$ ​is the mid-point of the ​line segment ​joining the points $P(-5,7)$ and $Q(-1,5)$, then ​the ​value ​of '$a$' is :

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

    (b) 6

    Step-by-step solution →
20. Q260 CBSE 2023
    The ​distance ​of the point $(3,5)$ ​from the $x$-axis ​is :

    1. (a)$3$
    2. (b)$4$
    3. (c)$5$
    4. (d)$\sqrt{31}$
    Show answer

    (c) $5$

    Step-by-step solution →