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 10 of 22

1. Q181 CBSE 2025
   Gurveer and Arushi built a robot that ​can paint a path as it moves on a ​graph paper. Some co-ordinate of points are marked on it. It starts from $(0,0)$, moves to the points listed in order (in ​straight lines) ​and ends at $(0,0)$. Arushi entered the points $P(8,6),Q(12,2),S(-6,6)$ in order. The path drawn ​by robot is ​shown in the figure. Based on the above, answer the following ​questions.

   1. iDetermine the distance $OP$.[1]
   2. ii$QS$ is represented by $2x+9y=42$. Find the co-ordinates of the point where it intersects $y$-axis.[1]
   3. iii(a)Point $R(4.8,y)$ divides the line segment $OP$ in a certain ratio. Find the ratio. Hence, find the value of $y$.[2]
   4. iii(b)Using distance formula, show that $\frac{PQ}{OS}=\frac{2}{3}$.[2]
   Show answer

   (i) $OP=10$ units; (ii) $\left(0,\frac{14}{3}\right)$; (iii)(a) $OR:RP=3:2$ and $y=\frac{18}{5}=3.6$; (iii)(b) $PQ=4\sqrt{2}$ and $OS=6\sqrt{2}$, so $\frac{PQ}{OS}=\frac{2}{3}$.

   Step-by-step solution →
2. Q182 CBSE 2025
   Case Study - 3 (Save Earth, Plant Trees). Trees act the natural filters. By ​planting trees ​in and around school premises, we create cleaner and ​healthier air ​for students and local residents, reducing respiratory problems. A school in Noida has proposed and organised a ​community drive on tree plantation under ​the title 'Save Earth, Plant Trees'. Students of that school have planted saplings in the field ​such that ​it formed a quadrilateral as shown in the figure ABCD. The coordinates from the graph are $A(-5,9)$, $B(2,3)$, $C(1,-5)$, $D(-6,1)$.

   1. (i)Find the distance between the two saplings at A and D.[1]
   2. (ii)(a)One student plants one sapling at the mid-point of AD. Then he moves along a straight line parallel to DB and sows another sapling on AB. What are the coordinates of the positions of these two new saplings?[2]
   3. (ii)(b) ORA new sapling is kept at a point M on DB such that DM:MB = 3:1. Find the coordinates of M.[2]
   4. (iii)The line segments AC and BD bisect each other at P(-2, 2). Find the coordinates of C.[1]
   Show answer

   (i) $AD=\sqrt{65}$ units $(\approx 8.06$ units$)$; (ii)(a) The sapling at the mid-point of $AD$ is at $\left(-\frac{11}{2},5\right)$ and the sapling on $AB$ is at $\left(-\frac{3}{2},6\right)$; (ii)(b) $M=\left(0,\frac{5}{2}\right)$; (iii) $C=(1,-5)$.

   Step-by-step solution →
3. Q183 CBSE 2025
   In a society, there is a circular park ​having ​two gates. The ​gates are ​placed ​at ​points $A(10,20)$ and $B(50,50)$, as shown in the figure below. Two fountains are installed at points $P$ and $Q$ ​on $AB$ such that $AP=PQ=QB$. Based on the above information, ​answer the following questions :

   1. iFind the coordinates of the centre C.[1]
   2. iiFind the radius of the circular park.[1]
   3. iii (a)Find the coordinates of the point P.[2]
   4. iii (b)Find the distance of the fountain at Q from gate A.[2]
   Show answer

   (i) $C(30,35)$; (ii) Radius $=25$ units; (iii)(a) $P\left(\frac{70}{3},30\right)$; (iii)(b) $AQ=\frac{100}{3}$ units $\approx 33.33$ units.

   Step-by-step solution →
4. Q184 CBSE 2024
   The ​distance between ​the ​points $(2,-1)$ and $(-1,-5)$ ​is :

   1. (a)15 units
   2. (b)5 units
   3. (c)25 units
   4. (d)41 units
   Show answer

   (b) 5 units

   Step-by-step solution →
5. Q185 CBSE 2024
   Point $P$ divides the line segment joining the points $A(4,-5)$ ​and $B(1,2)$ in ​the ​ratio $5:2$. ​Co-ordinates ​of ​point $P$ are

   1. (a)$\left(\frac{5}{2},\frac{-3}{2}\right)$
   2. (b)$\left(\frac{11}{7},0\right)$
   3. (c)$\left(\frac{13}{7},0\right)$
   4. (d)$\left(0,\frac{13}{7}\right)$
   Show answer

   (c) $\left(\frac{13}{7},0\right)$

   Step-by-step solution →
6. Q186 CBSE 2024
   If $C(1,-1)$ ​is ​the ​mid-point ​of ​the ​line ​segment AB joining points $A(4,x)$ ​and $B(-2,4)$, then value of x is :

   1. (a)5
   2. (b)$-5$
   3. (c)6
   4. (d)$-6$
   Show answer

   (d) $-6$

   Step-by-step solution →
7. Q187 CBSE 2024
   The distance between ​the points $A(-1,5)$ ​and $B(6,-2)$ ​is ​:

   1. (a)$2\sqrt{7}$
   2. (b)$7\sqrt{2}$
   3. (c)$49$
   4. (d)$14$
   Show answer

   (b) $7\sqrt{2}$

   Step-by-step solution →
8. Q188 CBSE 2024
   The ​mid-point of ​the ​line segment joining the ​points $(-1,3)$ ​and $\left(8,\frac{3}{2}\right)$ ​is:

   1. (a)$\left(\frac{7}{2},-\frac{3}{4}\right)$
   2. (b)$\left(\frac{7}{2},\frac{9}{2}\right)$
   3. (c)$\left(\frac{9}{2},-\frac{3}{4}\right)$
   4. (d)$\left(\frac{7}{2},\frac{9}{4}\right)$
   Show answer

   (d) $\left(\frac{7}{2},\frac{9}{4}\right)$

   Step-by-step solution →
9. Q189 CBSE 2024
   The coordinates ​of ​the mid-point of a line segment ​joining ​the points $A(3,-1)$ and $B(7,5)$ are $(5a,2b)$. The value of $(a+b)$ ​is ​:

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

   (c) 2

   Step-by-step solution →
10. Q190 CBSE 2024
    The ​distance ​of ​the ​point $(5,4)$ from ​the origin is

    1. (a)$41$
    2. (b)$\sqrt{41}$
    3. (c)$3$
    4. (d)$9$
    Show answer

    (b) $\sqrt{41}$

    Step-by-step solution →
11. Q191 CBSE 2024
    $AD$ is ​a ​median ​of $△ABC$ with ​vertices $A(5,-6)$, $B(6,4)$ ​and $C(0,0)$. Length $AD$ is ​equal to :

    1. (a)$\sqrt{68}$ units
    2. (b)$2\sqrt{15}$ units
    3. (c)$\sqrt{101}$ units
    4. (d)$10$ units
    Show answer

    (a) $\sqrt{68}$ units

    Step-by-step solution →
12. Q192 CBSE 2024
    The perpendicular ​bisector of the ​line ​segment joining the points $A(-1,3)$ ​and $B(2,4)$ ​cuts the ​y-axis at :

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

    (a) $(0,5)$

    Step-by-step solution →
13. Q193 CBSE 2024
    The ​distance ​between ​the ​points $(2,-3)$ and $(-2,3)$ is:

    1. (a)$2\sqrt{13}$ units
    2. (b)$5$ units
    3. (c)$13\sqrt{2}$ units
    4. (d)$10$ units
    Show answer

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

    Step-by-step solution →
14. Q194 CBSE 2024
    The distance ​between the ​points $A(0,-1)$ ​and $B(0,-9)$ ​is ​:

    1. (a)$6$
    2. (b)$8$
    3. (c)$4$
    4. (d)$2$
    Show answer

    (b) $8$

    Step-by-step solution →
15. Q195 CBSE 2024
    PQ is a diameter of ​a circle with ​centre $O(2,-4)$. ​If the coordinates of the point P are $(-4,5)$, then ​the coordinates ​of the point ​Q will ​be :

    1. (a)$(-3,4.5)$
    2. (b)$(-1,0.5)$
    3. (c)$(4,-5)$
    4. (d)$(8,-13)$
    Show answer

    (d) $(8,-13)$

    Step-by-step solution →
16. Q196 CBSE 2024
    The ​distance ​of $(-4,7)$ ​from ​the $y$-axis is:

    1. (a)$4$
    2. (b)$-4$
    3. (c)$7$
    4. (d)$\sqrt{65}$
    Show answer

    (a) $4$

    Step-by-step solution →
17. Q197 CBSE 2024
    The coordinates ​of ​a point ​on the $x$-axis, ​which is equidistant ​from $(-2,5)$ ​and $(2,-3)$ ​are:

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

    (d) $(-2,0)$

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18. Q198 CBSE 2024
    If $(a,6)$ ​is ​the ​mid-point of the line segment ​joining the ​points $A(-7,7)$ and $B(-3,5)$, then the value of $a$ is :

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

    (d) $-5$

    Step-by-step solution →
19. Q199 CBSE 2024
    If the coordinates ​of ​the ​mid-point of the ​line joining ​the points $(3a,4)$ ​and $(-2,2b)$ are $(5,a)$, ​then:

    1. (a)$a=2,b=5$
    2. (b)$a=4,b=2$
    3. (c)$a=3,b=4$
    4. (d)$a=5,b=8$
    Show answer

    (b) $a=4,b=2$

    Step-by-step solution →
20. Q200 CBSE 2024
    The ​distance of ​the point $P(3,-5)$ ​from the $x$-axis ​is ​:

    1. (a)$3$ units
    2. (b)$5$ units
    3. (c)$-5$ units
    4. (d)$\sqrt{34}$ units
    Show answer

    (b) $5$ units

    Step-by-step solution →