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 16 of 22

1. Q301 CBSE 2023
   In a classroom, ​4 ​friends Ravi, Vinod, Raghav and ​Vithal ​are seated at the points $A(2,3)$, $B(7,8)$, $C(10,5)$ and $D(5,0)$ respectively. ​Based on ​the above, answer ​the following questions :

   1. aFind the distance between Ravi and Raghav.[1]
   2. bFind the distance between Vinod and Vithal.[1]
   3. cShow that ABCD is a rectangle. OR Find the perimeter of rectangle ABCD.[2]
   Show answer

   (a) $AC=2\sqrt{17}$; (b) $BD=2\sqrt{17}$; (c) ABCD is a rectangle (diagonals equal); perimeter $=16\sqrt{2}\approx 22.63$.

   Step-by-step solution →
2. Q302 CBSE 2023
   Jagdish has a field which is in the ​shape of a right angled triangle AQC. ​He wants to ​leave a space in the form of a square PQRS inside the field for growing wheat and the remaining ​for growing vegetables ​(as shown in the figure). In ​the field, there is a pole marked ​as O. Based on the above information, answer the following questions :

   1. (i)Taking O as origin, coordinates of P are $(-200,0)$ and of Q are $(200,0)$. PQRS being a square, what are the coordinates of R and S?[1]
   2. (ii)(a)What is the area of square PQRS?[2]
   3. (ii)(b)OR What is the length of diagonal PR in square PQRS?[2]
   4. (iii)If S divides CA in the ratio $K:1$, what is the value of $K$, where point A is $(200,800)$?[1]
   Show answer

   $R=(200,400)$, $S=(-200,400)$; Area $=160000$ sq units; diagonal $PR=400\sqrt{2}\approx 565.69$ units; $K=1$.

   Step-by-step solution →
3. Q303 CBSE 2023
   Morning assembly is an integral part of every school's schedule. In the assembly, ​students always stand ​in rows and columns and this makes a coordinate ​system. In a school, there are $200$ students and they all assemble for prayer in $10$ rows. $4$ students are at $A$, $B$, $C$ and $D$ with the following positions of the coordinate system: $A(3,4)$, $B(6,7)$, $C(9,4)$ and $D(6,1)$. ​Based on ​the above, answer the following questions:

   1. (a)Find the distance between $A$ and $B$.
   2. (b)Find the distance between $C$ and $D$. ​
   3. (c)Show ​that $ABCD$ forms a parallelogram. OR ​Find the mid-point of the line segments $AC$ and $BD$.

   1. aFind the distance between $A$ and $B$.[1]
   2. bFind the distance between $C$ and $D$.[1]
   3. cShow that $ABCD$ forms a parallelogram.[2]
   4. c-ORFind the mid-point of the line segments $AC$ and $BD$. (OR alternative)[2]
   Show answer

   $AB=CD=3\sqrt{2}$; midpoints of $AC$ and $BD$ both $(6,4)$, so $ABCD$ is a parallelogram.

   Step-by-step solution →
4. Q304 CBSE 2023
   The ​coordinates ​of the vertices ​of a quadrilateral ABCD are given as $A(3,-1)$, $B(4,4)$, $C(-1,3)$ and $D(-2,-2)$. ​Find the ​following ​to know what ​type of quadrilateral it ​is :

   1. aFind the lengths of AB and CD.[1]
   2. bFind the lengths of BC and AD.[1]
   3. cFind the lengths of AC and BD. (OR) Find the mid-points of AC and BD.[2]
   Show answer

   (a) $AB=CD=\sqrt{26}$; (b) $BC=AD=\sqrt{26}$; (c) $AC=4\sqrt{2},BD=6\sqrt{2}$ (OR both midpoints $=(1,1)$). All sides equal, diagonals bisect each other and are unequal -> rhombus.

   Step-by-step solution →
5. Q305 CBSE 2020
   It is ​being given that the ​points $A(1,2)$, $B(0,0)$ ​and $C(a,b)$ are ​collinear. Which of the following relations ​between $a$ and $b$ is ​true ?

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

   (b) $2a=b$

   Step-by-step solution →
6. Q306 CBSE 2020
   The ​distance ​between the ​points $(-1,-3)$ ​and $(5,-2)$ is

   1. (a)$\sqrt{61}$ units
   2. (b)$\sqrt{37}$ units
   3. (c)$5$ units
   4. (d)$\sqrt{17}$ units
   Show answer

   (b) $\sqrt{37}$ units

   Step-by-step solution →
7. Q307 CBSE 2020
   The ​point on ​the x-axis which is ​equidistant ​from $(-4,0)$ and $(10,0)$ ​is

   1. (a)$(7,0)$
   2. (b)$(5,0)$
   3. (c)$(0,0)$
   4. (d)$(3,0)$
   Show answer

   (d) $(3,0)$

   Step-by-step solution →
8. Q308 CBSE 2020
   The centre ​of ​a ​circle ​whose ​end points ​of a diameter are $(-6,3)$ and $(6,4)$ is

   1. (a)$(8,-1)$
   2. (b)$(4,7)$
   3. (c)$\left(0,\frac{7}{2}\right)$
   4. (d)$\left(4,\frac{7}{2}\right)$
   Show answer

   (c) $\left(0,\frac{7}{2}\right)$

   Step-by-step solution →
9. Q309 CBSE 2020
   The ​mid-point ​of ​line ​segment joining ​the ​points $(-3,2)$ and $(7,6)$ ​is:

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

   (d) $(2,4)$

   Step-by-step solution →
10. Q310 CBSE 2020
    The distance ​(in units) ​of ​the ​point $(5,-6)$ from ​the ​x-axis is :

    1. (a)$6$
    2. (b)$4$
    3. (c)$\sqrt{61}$
    4. (d)$-6$
    Show answer

    (a) $6$

    Step-by-step solution →
11. Q311 CBSE 2020
    The ​distance between the ​points $(3,4)$ ​and $(-2,-1)$ ​is

    1. (a)$5\sqrt{2}$
    2. (b)$\sqrt{30}$
    3. (c)$6\sqrt{3}$
    4. (d)$\sqrt{10}$
    Show answer

    (a) $5\sqrt{2}$

    Step-by-step solution →
12. Q312 CBSE 2020
    If $(a,b)$ ​is the ​mid-point ​of ​the line segment ​joining the points $A(10,-6)$ and $B(k,4)$ ​and $a-2b=18$, the ​value of $k$ is

    1. (a)$30$
    2. (b)$22$
    3. (c)$4$
    4. (d)$40$
    Show answer

    (b) $22$

    Step-by-step solution →
13. Q313 CBSE 2020
    If $P\left(6,\frac{k}{2}\right)$ ​is ​the mid-point of the ​line segment ​joining ​the points $A(8,5)$ and $B(4,3)$, then the value ​of $k$ is

    1. (a)$-8$
    2. (b)$16$
    3. (c)$-6$
    4. (d)$8$
    Show answer

    (d) $8$

    Step-by-step solution →
14. Q314 CBSE 2020
    The point $P$ on $x$-axis equidistant ​from ​the ​points $A(-1,0)$ ​and $B(5,0)$ ​is

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

    (a) $(2,0)$

    Step-by-step solution →
15. Q315 CBSE 2020
    The distance ​between the ​points $(a\cos \theta +b\sin \theta ,0)$ and $(0,a\sin \theta -b\cos \theta )$ ​is

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

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

    Step-by-step solution →
16. Q316 CBSE 2020
    The ​value of $k$ for which ​the ​points $A(0,1)$, $B(2,k)$ and $C(4,-5)$ are ​collinear ​is

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

    (b) $-2$

    Step-by-step solution →
17. Q317 CBSE 2020
    The perimeter of ​a ​triangle ​with ​vertices $(0,4)$, $(0,0)$ ​and $(3,0)$ ​is

    1. (a)$7+\sqrt{5}$
    2. (b)$5$
    3. (c)$10$
    4. (d)$12$
    Show answer

    (d) $12$

    Step-by-step solution →
18. Q318 CBSE 2020
    The ​distance ​between ​the ​points $(m,-n)$ ​and $(-m,n)$ is

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

    (c) $2\sqrt{m^2+n^2}$

    Step-by-step solution →
19. Q319 CBSE 2020
    The distance of the point $(-12,5)$ ​from ​the origin ​is

    1. (a)$12$
    2. (b)$5$
    3. (c)$13$
    4. (d)$169$
    Show answer

    (c) $13$

    Step-by-step solution →
20. Q320 CBSE 2020
    The ​co-ordinates ​of ​the point which ​is reflection of ​point $(-3,5)$ ​in $x$-axis are

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

    (c) $(-3,-5)$

    Step-by-step solution →