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 6 of 22

1. Q101 CBSE 2026
   A $(-2,3)$ and B $(4,1)$ are end ​points of the ​diameter of a ​semi-circle. ​The semi-circle intersects the $y$-axis at point P. Find ​the co-ordinates ​of ​the point ​P.
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   $P=(0,5)$ or $P=(0,-1)$ — the two points where the circle on diameter $AB$ meets the $y$-axis.

   Step-by-step solution →
2. Q102 CBSE 2026
   Diagonals $AC$ ​and $BD$ of ​square $ABCD$ ​intersect at $P$. Coordinates of points $B$ and $D$ ​are $(9,-2)$ and $(1,6)$ respectively.

   1. (i)Find the co-ordinates of point $P$.
   2. (ii)​Find the length of the side ​of the ​square.

   Show answer

   (i) The coordinates of $P$ are $(5,2)$. (ii) The length of the side of the square is $8$ units.

   Step-by-step solution →
3. Q103 CBSE 2026
   Find ​the coordinates of a ​point ​on the line $x+y=5$ ​which is ​equidistant from $(6,4)$ and $(5,2)$.
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   The required point is $\left(-\frac{3}{2},\frac{13}{2}\right)$, i.e. $(-1.5,6.5)$.

   Step-by-step solution →
4. Q104 CBSE 2026
   Find the ​ratio ​in ​which ​the $x$-axis divides the line segment ​joining the points $(-6,5)$ and $(-4,-1)$. Also, ​find the point of ​intersection.
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   The $x$-axis divides the line segment in the ratio $5:1$, and the point of intersection is $\left(-\frac{13}{3},0\right)$.

   Step-by-step solution →
5. Q105 CBSE 2026
   Find ​the coordinates of the ​points ​of ​trisection of the ​line ​segment joining the points $A(-1,4)$ ​and $B(-3,-2)$.
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   The points of trisection are $\left(-\frac{5}{3},2\right)$ and $\left(-\frac{7}{3},0\right)$.

   Step-by-step solution →
6. Q106 CBSE 2026
   Points $P(6,0)$, $Q(2,8)$ and $R(-2,4)$ are vertices of $△PQR$. It is ​given ​that $MN\parallel QR$ ​such that $\frac{PM}{MQ}=\frac{1}{3}$. Using distance ​formula ​and ​ratio ​formula, show ​that $\frac{MN}{QR}=\frac{1}{4}$.

   Show answer

   $MN=\sqrt{2}$, $QR=4\sqrt{2}$, so $\frac{MN}{QR}=\frac{1}{4}$, as required.

   Step-by-step solution →
7. Q107 CBSE 2026
   Find ​the coordinates of the points of ​trisection ​of the ​line segment joining the ​points $P(5,-4)$ and $Q(-4,2)$.
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   The points of trisection are $(2,-2)$ and $(-1,0)$.

   Step-by-step solution →
8. Q108 CBSE 2026
   Find the ​ratio ​in which the ​point P $(6,k)$ ​divides the ​line segment joining ​the points M $(4,2)$ and N $(8,-4)$. ​Hence find the value of $k$.
   Show answer

   P divides MN in the ratio $1:1$ (P is the midpoint), and $k=-1$.

   Step-by-step solution →
9. Q109 CBSE 2026
   Find a ​relation between $x$ ​and $y$ such that ​the point $P(x,y)$ is ​equidistant ​from ​the points $A(5,3)$ and $B(1,7)$.
   Show answer

   The required relation is $x-y+2=0$ (equivalently $y=x+2$), which is the perpendicular bisector of $AB$.

   Step-by-step solution →
10. Q110 CBSE 2026
    If the point $P(x,y)$ ​is equidistant from the ​points $(3,6)$ and $(-3,4)$, ​obtain the relation between $x$ and $y$. ​Hence, ​find the coordinates ​of point $P$ if ​it lies on $x$-axis.
    Show answer

    The relation between $x$ and $y$ is $3x+y=5$; when $P$ lies on the $x$-axis ($y=0$), its coordinates are $P\left(\frac{5}{3},0\right)$.

    Step-by-step solution →
11. Q111 CBSE 2026
    Show that the quadrilateral $ABCD$ with vertices $A(0,3)$, $B(-2,0)$, $C(0,-5)$ ​and $D(2,0)$ is ​a kite. Also, find the length ​of each diagonal of ​the kite $ABCD$.
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    $ABCD$ is a kite because $AB=AD=\sqrt{13}$ units and $CB=CD=\sqrt{29}$ units - two distinct pairs of equal adjacent sides. The diagonals measure $AC=8$ units and $BD=4$ units.

    Step-by-step solution →
12. Q112 CBSE 2026
    Show that ​the ​quadrilateral $ABCD$ ​formed by ​joining the points $A(-2,-1)$, $B(1,-1)$, $C(1,2)$ ​and $D(-2,2)$ in order is a ​square.
    Show answer

    $AB=BC=CD=DA=3$ units and $AC=BD=3\sqrt{2}$ units, so all four sides are equal and the diagonals are equal; hence $ABCD$ is a square.

    Step-by-step solution →
13. Q113 CBSE 2026
    Find ​the ​coordinates of the points which ​divide the ​line segment ​joining points $P(-1,7)$ ​and $Q(4,-3)$ into ​three equal ​parts.
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    The two points are $\left(\frac{2}{3},\frac{11}{3}\right)$ and $\left(\frac{7}{3},\frac{1}{3}\right)$.

    Step-by-step solution →
14. Q114 CBSE 2026
    A circle ​centered ​at $(2,1)$ passes through the ​points $A(5,6)$ ​and $B(-3,K)$. Find the ​value(s) of $K$. Hence find length ​of chord $AB$.
    Show answer

    $K=4$ or $K=-2$. For $K=4$, $AB=2\sqrt{17}$ units; for $K=-2$, $AB=8\sqrt{2}$ units.

    Step-by-step solution →
15. Q115 CBSE 2026
    Prove ​that the point $P$ dividing the line segment joining the ​points $A(-1,7)$ and $B(4,-3)$ in the ratio $3:2$ ​lies ​on ​the line $x-3y=-1$. Also ​find the ​length of $PA$ and $PB$.
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    $P=(2,1)$, and since $2-3(1)=-1$, the point $P$ lies on the line $x-3y=-1$. The lengths are $PA=3\sqrt{5}$ units and $PB=2\sqrt{5}$ units.

    Step-by-step solution →
16. Q116 CBSE 2026
    A point $P(x,7)$ divides ​a line segment ​joining ​the points $A(-5,4)$ and $B(7,9)$ ​in a ​certain ​ratio. Find the ratio ​and hence find the ​value of $x$.
    Show answer

    $P$ divides $AB$ in the ratio $3:2$, and $x=\frac{11}{5}$ (that is, $x=2.2$).

    Step-by-step solution →
17. Q117 CBSE 2026
    The ​vertices of a rhombus $ABCD$ are $A(-3,-4)$, $B(5,-3)$, $C(1,4)$ and $D(-7,3)$. Find ​the length ​of ​both the diagonals. ​Hence, find area ​of ​the rhombus $ABCD$.
    Show answer

    Diagonals: $AC=4\sqrt{5}$ units and $BD=6\sqrt{5}$ units; area of rhombus $ABCD=60$ square units.

    Step-by-step solution →
18. Q118 CBSE 2026
    The line segment joining the ​points $A(-5,1)$ and $B(7,6)$ is trisected ​at the points $P$ ​and $Q$ such ​that $P$ is nearer to $A$. If $P$ ​lies on the ​line $x+y=k$, then ​find ​the value of $k$.
    Show answer

    $P=\left(-1,\frac{8}{3}\right)$ and $k=\frac{5}{3}$.

    Step-by-step solution →
19. Q119 CBSE 2026
    In the school garden, Arun (A), Babu (B), Chandra (C) ​and ​Daya (D) planted ​flower plants of Sunflower, Rose, ​Champa and Jasmine ​respectively ​at point $A(2,8)$, $B(7,8)$, $C(9,3)$ and $D(2,3)$ respectively. Based on the ​above, answer the following questions:

    1. (i)Find the distances $AB$ and $AD$.
    2. (ii)Find $BC-CD$.
    3. (iii)(a)If Varun wants to plant his flower plant at a point $M$ such that $DM:MC=3:2$, find the coordinates of $M$.
    4. (iii)(b)OR: If $N$ divides the line segment $AC$ in the ratio $2:3$, find the coordinates of $N$.
    Show answer

    (i) $AB=5$ units and $AD=5$ units; (ii) $BC-CD=\sqrt{29}-7\approx -1.61$ units; (iii)(a) $M=\left(\frac{31}{5},3\right)=(6.2,3)$; (iii)(b) $N=\left(\frac{24}{5},6\right)=(4.8,6)$.

    Step-by-step solution →
20. Q120 CBSE 2026
    Observe the map ​of ​Jaipur city placed on ​a Cartesian ​plane. Taking Rambagh Palace as ​origin, ​the location ​of some places ​are given below : Point A : $(-4,2)$ Rajasthan High Court Point B : $(4,-4)$ Birla Mandir Point C : $(4,3)$ Heera Bagh Point D : $(-5,-2)$ Amar Jawan Jyoti Based on the above, answer the following questions :

    1. (i)Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home?[1]
    2. (ii)There is a crossing on X-axis which divides $AD$ in a certain ratio. Find the ratio.[1]
    3. (iii) (a)Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti? Justify your answer.[2]
    4. (iii) (b)OR — Using section formula, show that points $A$, $O$ and $B$ are not collinear.[2]
    Show answer

    (i) Rehana covers $2\sqrt{65}\approx 16.12$ units daily. (ii) The x-axis divides $AD$ in the ratio $1:1$. (iii)(a) No — $BC=7$ but $BD=\sqrt{85}$, so Birla Mandir is not equidistant from Heera Bagh and Amar Jawan Jyoti. (iii)(b) Assuming $O$ divides $AB$ in ratio $k:1$ gives $k=1$ from the $x$-coordinate but $k=\frac{1}{2}$ from the $y$-coordinate; the mismatch shows $A$, $O$, $B$ are not collinear.

    Step-by-step solution →