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 19 of 22

1. Q361 CBSE 2019
   Points $P$ ​and $Q$ ​trisect the line segment joining the points $A(-2,0)$ and $B(0,8)$ such that $P$ ​is near to $A$. Find the coordinates of points $P$ ​and $Q$.
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   $P\left(-\frac{4}{3},\frac{8}{3}\right)$ and $Q\left(-\frac{2}{3},\frac{16}{3}\right)$

   Step-by-step solution →
2. Q362 CBSE 2019
   The mid-point of ​the line ​segment ​joining $A(2a,4)$ ​and $B(-2,3b)$ is $(1,2a+1)$. ​Find the values ​of $a$ ​and $b$.
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   $a=2$ and $b=2$.

   Step-by-step solution →
3. Q363 CBSE 2019
   Find ​a relation between $x$ ​and $y$ ​if ​the points $A(x,y)$, $B(-4,6)$ ​and $C(-2,3)$ are ​collinear.
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   The required relation is $3x+2y=0$.

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4. Q364 CBSE 2019
   Find the ​area ​of ​a triangle ​whose vertices are given ​as $(1,-1)$, $(-4,6)$ and $(-3,-5)$.
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   $24$ square units

   Step-by-step solution →
5. Q365 CBSE 2019
   Find the ratio in ​which the segment joining ​the points $(1,-3)$ and $(4,5)$ is divided ​by $x$-axis? ​Also ​find ​the ​coordinates of this ​point on $x$-axis.
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   The $x$-axis divides the segment in the ratio $3:5$, and the point is $\left(\frac{17}{8},0\right)$.

   Step-by-step solution →
6. Q366 CBSE 2019
   Find the ​co-ordinates of ​the point which ​divides the line segment joining the points $(-3,2)$ and $(-8,7)$ ​in ​the ratio $2:3$ ​internally.
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   The required point is $(-5,4)$.

   Step-by-step solution →
7. Q367 CBSE 2019
   The point ​R divides ​the ​line segment ​AB, where $A(-4,0)$ and $B(0,6)$ ​such ​that $AR=\frac{3}{4}AB$. Find the ​coordinates ​of R.
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   $R=\left(-1,\frac{9}{2}\right)$, i.e. $(-1,4.5)$.

   Step-by-step solution →
8. Q368 CBSE 2019
   In what ratio does ​the ​point $P(-4,y)$ divide ​the line segment ​joining the points $A(-6,10)$ and $B(3,-8)$? ​Hence find ​the value of $y$.
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   $P$ divides $AB$ in the ratio $2:7$, and $y=6$.

   Step-by-step solution →
9. Q369 CBSE 2019
   Points $A(5,-1)$, $B(-3,2)$ and $C(-1,8)$ ​are the vertices of ​a $△ABC$. ​Find the length of ​the ​median ​from $A$.
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   The length of the median from $A$ is $\sqrt{85}\approx 9.22$ units.

   Step-by-step solution →
10. Q370 CBSE 2019
    Find the ​area of a rhombus whose vertices taken ​in order ​are ​the ​points $(3,0)$, $(4,5)$, $(-1,4)$ ​and $(-2,-1)$.
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    The area of the rhombus is $24$ square units.

    Step-by-step solution →
11. Q371 CBSE 2019
    Find ​the ​value ​of $p$ for ​which the ​points $(-5,1)$, $(1,p)$ ​and $(4,-2)$ are collinear.
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    $p=-1$.

    Step-by-step solution →
12. Q372 CBSE 2019
    Find the area of the triangle formed ​by ​joining the mid-points of ​the sides of ​the ​triangle $ABC$, whose vertices ​are $A(0,-1)$, $B(2,1)$ and $C(0,3)$.
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    The area of the medial triangle is $1$ square unit.

    Step-by-step solution →
13. Q373 CBSE 2019
    Point $P$ divides the ​line ​segment ​joining the points $A(2,1)$ and $B(5,-8)$ such that $\frac{AP}{AB}=\frac{1}{3}$. 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 →
14. Q374 CBSE 2019
    For what value ​of $p$, ​are the ​points $(2,1)$, $(p,-1)$ ​and $(-1,3)$ collinear?
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    $p=5$.

    Step-by-step solution →
15. Q375 CBSE 2019
    Find ​the ratio ​in which the line $x-3y=0$ divides the ​line segment joining ​the points $(-2,-5)$ and $(6,3)$. ​Find the ​coordinates of the point ​of intersection.
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    The line divides the segment in the ratio $13:3$, and the point of intersection is $\left(\frac{9}{2},\frac{3}{2}\right)$.

    Step-by-step solution →
16. Q376 CBSE 2019
    Find ​the ​point on $y$-axis ​which ​is ​equidistant from the ​points $(5,-2)$ and $(-3,2)$.
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    The required point is $(0,-2)$.

    Step-by-step solution →
17. Q377 CBSE 2019
    The line segment joining the points $A(2,1)$ and $B(5,-8)$ is ​trisected at ​the ​points $P$ and $Q$ such that $P$ is ​nearer to $A$. If $P$ also ​lies on ​the line ​given ​by $2x-y+k=0$, find the value of $k$.
    Show answer

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

    Step-by-step solution →
18. Q378 CBSE 2018
    Find ​the value of $y$ ​for which the distance ​between the ​points $(2,-3)$ and $(10,y)$ ​is $10$ units.
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    $y=3$ or $y=-9$

    Step-by-step solution →
19. Q379 CBSE 2018
    Find ​the distance ​of a ​point $P(x,y)$ ​from ​the origin.
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    The distance of $P(x,y)$ from the origin is $\sqrt{x^2+y^2}$.

    Step-by-step solution →
20. Q380 CBSE 2018
    If the point $(0,2)$ is ​equidistant ​from the points $(3,k)$ ​and $(k,5)$, ​find ​the value of $k$.
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    $k=1$

    Step-by-step solution →