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 20 of 22

1. Q381 CBSE 2018
   Find ​the ​ratio ​in which $P(4,m)$ ​divides the line segment ​joining ​the ​points $A(2,3)$ and $B(6,-3)$. Hence ​find $m$.
   Show answer

   P divides AB in the ratio $1:1$, and $m=0$.

   Step-by-step solution →
2. Q382 CBSE 2018
   If $A(-5,7)$, $B(-4,-5)$, $C(-1,-6)$ ​and $D(4,5)$ are ​the ​vertices ​of a quadrilateral, ​find the area of the ​quadrilateral $ABCD$.
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   Area of quadrilateral $ABCD=17.5+54.5=72$ square units.

   Step-by-step solution →
3. Q383 CBSE 2018
   The line segment joining the points $A(2,1)$ and $B(5,-8)$ ​is ​trisected ​at the ​points $P$ and $Q$, ​where $P$ is nearer to $A$. ​If $P$ ​lies on the line $2x-y+k=0$, find the value of $k$.
   Show answer

   $k=-8$ (with $P=(3,-2)$).

   Step-by-step solution →
4. Q384 CBSE 2018
   The $x$-coordinate ​of ​a point $P$ ​is twice its $y$-coordinate. ​If $P$ is equidistant from ​the points $Q(2,-5)$ ​and $R(-3,6)$, find the coordinates of $P$.
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   $P=(16,8)$

   Step-by-step solution →
5. Q385 CBSE 2018
   If $A(-2,1)$, $B(a,0)$, $C(4,b)$ ​and $D(1,2)$ are the ​vertices of a ​parallelogram $ABCD$, ​find the values of $a$ ​and $b$. ​Hence find ​the lengths ​of its sides.
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   $a=1$, $b=1$; each side has length $\sqrt{10}$ units ($AB=BC=CD=DA=\sqrt{10}$).

   Step-by-step solution →
6. Q386 CBSE 2017
   If the ​distance between the ​points $(4,k)$ and $(1,0)$ is $5$, then what ​can be ​the ​possible values ​of $k$?
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   $k=4$ or $k=-4$.

   Step-by-step solution →
7. Q387 CBSE 2017
   Find ​the ​coordinates of the point on ​the $x$-axis, ​which is ​equidistant from the points $(-2,5)$ ​and $(2,-3)$.
   Show answer

   The required point on the $x$-axis is $(-2,0)$.

   Step-by-step solution →
8. Q388 CBSE 2017
   A line ​intersects ​the $y$-axis and $x$-axis ​at the points $P$ and $Q$ ​respectively. ​If $(2,-5)$ is the mid-point ​of $PQ$, then find the coordinates of $P$ ​and $Q$.
   Show answer

   $P=(0,-10)$ and $Q=(4,0)$

   Step-by-step solution →
9. Q389 CBSE 2017
   Find the coordinates ​of the ​points of ​trisection of the line ​segment joining ​the ​points $A(7,-2)$ and $B(1,-5)$.
   Show answer

   The points of trisection are $(5,-3)$ and $(3,-4)$.

   Step-by-step solution →
10. Q390 CBSE 2017
    A ​line ​intersects the y-axis and x-axis at ​the ​points $P$ ​and $Q$ respectively. If $(2,-5)$ is the mid-point of $PQ$, then ​find the ​coordinates of $P$ and $Q$.
    Show answer

    $P=(0,-10)$ and $Q=(4,0)$.

    Step-by-step solution →
11. Q391 CBSE 2017
    If two adjacent ​vertices of ​a parallelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2,-5)$, ​then find the coordinates ​of ​the ​other two vertices.
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    The other two vertices are $C(1,-12)$ and $D(5,-10)$.

    Step-by-step solution →
12. Q392 CBSE 2017
    If the ​distances of $P(x,y)$ from $A(5,1)$ ​and $B(-1,5)$ ​are ​equal, ​then prove ​that $3x=2y$.
    Show answer

    Setting $P{A}^2=P{B}^2$ and simplifying gives $3x=2y$, as required.

    Step-by-step solution →
13. Q393 CBSE 2017
    Find ​the ​coordinates of the points of ​trisection of the ​line ​segment joining ​the points $(3,-2)$ and $(-3,-4)$.
    Show answer

    The points of trisection are $P\left(1,-\frac{8}{3}\right)$ and $Q\left(-1,-\frac{10}{3}\right)$.

    Step-by-step solution →
14. Q394 CBSE 2017
    In ​what ratio does the point $\left(\frac{24}{11},y\right)$ divide the ​line segment joining ​the points $P(2,-2)$ ​and $Q(3,7)$? ​Also find the ​value of $y$.
    Show answer

    The point divides $PQ$ in the ratio $2:9$, and $y=-\frac{4}{11}$.

    Step-by-step solution →
15. Q395 CBSE 2017
    In what ​ratio ​does ​the point $\left(\frac{24}{11},y\right)$ divide the line segment joining the points $P(2,-2)$ ​and $Q(3,7)$? ​Also ​find the value of $y$.
    Show answer

    The point divides $PQ$ in the ratio $2:9$, and $y=-\frac{4}{11}$.

    Step-by-step solution →
16. Q396 CBSE 2017
    Show that $△ABC$, ​where $A(-2,0)$, $B(2,0)$, $C(0,2)$ ​and $△PQR$ ​where $P(-4,0)$, $Q(4,0)$, $R(0,4)$ ​are ​similar ​triangles.
    Show answer

    Since $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}=\frac{1}{2}$, by the SSS criterion $△ABC\sim △PQR$.

    Step-by-step solution →
17. Q397 CBSE 2017
    The ​mid-points of the ​sides $BC$, $CA$ and $AB$ of ​a $△ABC$ are $D(3,4)$, $E(8,9)$ ​and $F(6,7)$ respectively. Find the ​coordinates of the ​vertices of the ​triangle.
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    The vertices are $A(11,12)$, $B(1,2)$ and $C(5,6)$.

    Step-by-step solution →
18. Q398 CBSE 2017
    The area ​of ​a triangle is $5$ ​sq units. ​Two ​of its ​vertices are $(2,1)$ and $(3,-2)$. If the third vertex is $\left(\frac{7}{2},y\right)$, find ​the value ​of $y$.
    Show answer

    $y=\frac{13}{2}$ (i.e. $6.5$) or $y=-\frac{27}{2}$ (i.e. $-13.5$).

    Step-by-step solution →
19. Q399 CBSE 2017
    In ​the given ​figure, $△ABC$ is ​an ​equilateral triangle of side $3$ units. Find ​the coordinates ​of the other two ​vertices.

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    $B=(5,0)$ and $C=\left(\frac{7}{2},\frac{3\sqrt{3}}{2}\right)$, i.e. $C\approx (3.5,2.6)$.

    Step-by-step solution →
20. Q400 CBSE 2017
    Show that $△ABC$ ​with ​vertices $A(-2,0)$, $B(0,2)$ and $C(2,0)$ ​is ​similar to $△DEF$ with vertices $D(-4,0)$, $F(4,0)$ ​and $E(0,4)$.
    Show answer

    All three pairs of corresponding sides satisfy $\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}=\frac{1}{2}$, so by the SSS criterion $△ABC\sim △DEF$ (hence proved).

    Step-by-step solution →