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 12 of 22

1. Q221 CBSE 2024
   Find the ratio in which ​the Y-axis divides ​the ​line ​segment ​joining the ​points $A(5,-6)$ and $B(-1,-4)$. Also, find the point of ​intersection.
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   The Y-axis divides $AB$ in the ratio $5:1$, and the point of intersection is $\left(0,-\frac{13}{3}\right)$.

   Step-by-step solution →
2. Q222 CBSE 2024
   Find the ​ratio ​in which the ​point $P(-4,6)$ divides ​the line segment joining ​the ​points $A(-6,10)$ and $B(3,-8)$.
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   The point $P(-4,6)$ divides the segment $AB$ internally in the ratio $2:7$.

   Step-by-step solution →
3. Q223 CBSE 2024
   Prove that ​the ​points $(3,0)$, $(6,4)$ ​and $(-1,3)$ are ​the vertices ​of ​an isosceles triangle.
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   $AB=CA=5$ units and $BC=5\sqrt{2}$ units, so two sides are equal and the points form an isosceles triangle. Hence proved.

   Step-by-step solution →
4. Q224 CBSE 2024
   In ​what ratio is the line segment ​joining the points $(3,-5)$ ​and $(-1,6)$ ​divided by ​the ​line $y=x$ ?
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   The line $y=x$ divides the segment joining $(3,-5)$ and $(-1,6)$ internally in the ratio $8:7$ (measured from $(3,-5)$), at the point $\left(\frac{13}{15},\frac{13}{15}\right)$.

   Step-by-step solution →
5. Q225 CBSE 2024
   $A(3,0)$, $B(6,4)$ ​and $C(-1,3)$ ​are ​vertices ​of ​a triangle $ABC$. ​Find length of its median $BE$.
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   $BE=\frac{5\sqrt{5}}{2}$ units $\approx 5.59$ units

   Step-by-step solution →
6. Q226 CBSE 2024
   Determine ​the ​ratio ​in which the ​point $(-6,y)$ ​divides the line segment joining ​the ​points $A(-3,-1)$ and $B(-8,9)$. Also, find the value of $y$.
   Show answer

   The point divides $AB$ internally in the ratio $3:2$, and $y=5$.

   Step-by-step solution →
7. Q227 CBSE 2024
   Find the ratio in which ​the point $\left(\frac{8}{5},y\right)$ divides ​the line segment joining ​the ​points $(1,2)$ ​and $(2,3)$. Also, find ​the ​value of $y$.
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   The point divides the segment internally in the ratio $3:2$, and $y=\frac{13}{5}$.

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8. Q228 CBSE 2024
   $ABCD$ is a ​rectangle formed by ​the points $A(-1,-1)$, $B(-1,6)$, $C(3,6)$ and $D(3,-1)$. $P,Q,R$ and $S$ are mid-points of ​sides $AB,BC,CD$ ​and $DA$ respectively. ​Show that diagonals of ​the ​quadrilateral $PQRS$ bisect each other.
   Show answer

   Mid-point of $PR$ = mid-point of $QS$ = $\left(1,\frac{5}{2}\right)$, so the diagonals of $PQRS$ bisect each other. Hence proved.

   Step-by-step solution →
9. Q229 CBSE 2024
   If $A(2,-2)$, $B(7,3)$, $C(11,-1)$ ​and $D(6,-6)$ are ​the ​vertices of ​a ​quadrilateral $ABCD$, then ​find what ​type of ​quadrilateral $ABCD$ is.
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   $ABCD$ is a rectangle: its opposite sides are equal ($AB=CD=5\sqrt{2}$, $BC=DA=4\sqrt{2}$) and its diagonals are equal ($AC=BD=\sqrt{82}$). It is not a square, because the adjacent sides $5\sqrt{2}$ and $4\sqrt{2}$ are unequal.

   Step-by-step solution →
10. Q230 CBSE 2024
    Find the co-ordinates of ​the ​points ​of trisection ​of the line segment joining ​the ​points $(-2,2)$ and $(7,-4)$.
    Show answer

    The points of trisection are $P(1,0)$ and $Q(4,-2)$.

    Step-by-step solution →
11. Q231 CBSE 2024
    Find the ​ratio in which ​the ​line segment ​joining ​the points $(5,3)$ ​and $(-1,6)$ ​is divided by Y-axis.
    Show answer

    The Y-axis divides the line segment joining $(5,3)$ and $(-1,6)$ internally in the ratio $5:1$, at the point $\left(0,\frac{11}{2}\right)$.

    Step-by-step solution →
12. Q232 CBSE 2024
    $P(-2,5)$ and $Q(3,2)$ ​are two points. Find the ​coordinates of the ​point R ​on line ​segment ​PQ such ​that $PR=2QR$.
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    The required point is $R\left(\frac{4}{3},3\right)$.

    Step-by-step solution →
13. Q233 CBSE 2024
    Find ​the coordinates of ​the points of trisection ​of ​the line ​segment joining ​the points $A(5,-3)$ and $B(-4,3)$.
    Show answer

    The points of trisection are $P(2,-1)$, nearer to $A$, and $Q(-1,1)$, nearer to $B$.

    Step-by-step solution →
14. Q234 CBSE 2024
    Find the relation between $x$ and $y$ ​such ​that ​the ​point $P(x,y)$ is equidistant ​from ​the points $A(7,1)$ and $B(3,5)$.
    Show answer

    The required relation is $x-y=2$ (equivalently $x-y-2=0$).

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15. Q235 CBSE 2024
    Find ​the coordinates ​of ​the points of trisection of the ​line segment joining the points $A(2,-2)$ and $B(-7,4)$.
    Show answer

    The points of trisection are $P(-1,0)$, nearer to $A$, and $Q(-4,2)$, nearer to $B$.

    Step-by-step solution →
16. Q236 CBSE 2024
    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

    The points that divide $AB$ into four equal parts are $\left(-1,\frac{7}{2}\right)$, $(0,5)$ and $\left(1,\frac{13}{2}\right)$.

    Step-by-step solution →
17. Q237 CBSE 2024
    The vertices ​of a quadrilateral ​ABCD ​are $A(6,-2)$, $B(9,2)$, $C(5,-1)$ ​and $D(2,-5)$. ​Prove that ABCD is a ​rhombus, and not ​a square.
    Show answer

    $AB=BC=CD=DA=5$, so ABCD is a rhombus. Its diagonals $AC=\sqrt{2}$ and $BD=7\sqrt{2}$ are unequal, so it is not a square. Hence proved.

    Step-by-step solution →
18. Q238 CBSE 2024
    Ryan, ​from ​a very young age, was fascinated by the twinkling ​of stars and the vastness ​of space. He always dreamt of becoming an astronaut one day. So he started to sketch his ​own rocket designs on the graph ​sheet. One such design is given below (see figure). Based on the above, ​answer the following questions.

    1. (i)Find the mid-point of the segment joining $F$ and $G$.[1]
    2. (ii)(a)What is the distance between the points $A$ and $C$ ?[2]
    3. (ii)(b)Find the coordinates of the point which divides the line segment joining the points $A$ and $B$ in the ratio $1:3$ internally. (OR)[2]
    4. (iii)What are the coordinates of the point $D$ ?[1]
    Show answer

    (i) The mid-point of $FG$ is $(-1,2)$; (ii)(a) $AC=2\sqrt{13}$ units ($\approx 7.21$ units); OR (ii)(b) The point is $\left(3,\frac{7}{2}\right)$; (iii) $D=(-2,-5)$.

    Step-by-step solution →
19. Q239 CBSE 2024
    A garden is in ​the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at ​the ​distance of $1$ m from each other. He wants to decorate the garden with rose plants. ​He chose a triangular region inside the garden to grow rose ​plants. In the above situation, the gardener took ​help from the students of class $10$. ​They made a chart for ​it which looks like the given figure. Based on the above, answer the following questions :

    1. (i)If A is taken as origin, what are the coordinates of the vertices of $△PQR$?[1]
    2. (ii)(a)Find distances $PQ$ and $QR$.[2]
    3. (ii)(b)OR Find the coordinates of the point which divides the line segment joining points $P$ and $R$ in the ratio $2:1$ internally.[2]
    4. (iii)Find out if $△PQR$ is an isosceles triangle.[1]
    Show answer

    (i) $P(4,6)$, $Q(3,2)$, $R(6,5)$; (ii)(a) $PQ=\sqrt{17}$ m and $QR=3\sqrt{2}$ m; OR (ii)(b) The point is $\left(\frac{16}{3},\frac{16}{3}\right)$; (iii) No, $△PQR$ is not isosceles: its sides $\sqrt{17}$ m, $3\sqrt{2}$ m and $\sqrt{5}$ m are all different.

    Step-by-step solution →
20. Q240 CBSE 2024
    Drones are ​used by military for surveillance purposes. These days, drones are also used by individual entrepreneurs, SMEs and large ​companies to accomplish various other tasks (disaster management, entertainment, law enforcement, wildlife monitoring, weather ​forecast, aerial photograph, shipping and delivery, geographical mapping, precision agriculture, search and rescue, etc.). A drone is flying over a rectangular ​field with vertices at A(-100, 0), B(100, 0), ​C(100, 150) and D(-100, 150). ​The drone captures an image at a location (x, ​y).

    1. (i)Find the dimensions of the rectangular field.[1]
    2. (ii)Find the distance between points A and C.[1]
    3. (iii)(a)If a drone captures the image of an object $P(x,y)$ on the rectangular field, find the relation between $x$ and $y$ such that $PA=PC$.[2]
    4. (iii)(b)If a drone captures the image of an object at a point Q whose x-coordinate is 0 and it is equidistant from points A and D, find the coordinates of Q.[2]
    Show answer

    (i) Length $AB=200$ units and breadth $BC=150$ units, so the field is $200\times 150$ units; (ii) $AC=250$ units; (iii)(a) $4x+3y=225$; (iii)(b) $Q(0,75)$.

    Step-by-step solution →