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 15 of 22

1. Q281 CBSE 2023
   Find the ​value(s) ​of 'x' so ​that $PQ=QR$, where the ​coordinates ​of P, Q and ​R are $(6,-1)$, $(1,3)$ and $(x,8)$ respectively.
   Show answer

   $x=5$ or $x=-3$

   Step-by-step solution →
2. Q282 CBSE 2023
   The vertices ​of a ​triangle ​are $(-2,0)$, $(2,3)$ ​and $(1,-3)$. Is ​the triangle equilateral, isosceles ​or ​scalene ?
   Show answer

   All three sides differ, so the triangle is scalene.

   Step-by-step solution →
3. Q283 CBSE 2023
   Find ​the ​ratio in which ​the $y$-axis ​divides the line segment joining ​the points $A(5,-6)$ and $B(-1,-4)$.
   Show answer

   The y-axis divides $AB$ in the ratio $5:1$.

   Step-by-step solution →
4. Q284 CBSE 2023
   Find ​the ratio in ​which the $y$-axis ​divides the ​line ​segment joining the points $(5,-6)$ ​and $(-1,-4)$. Also, find the point of intersection.
   Show answer

   Ratio $5:1$; point $\left(0,-\frac{13}{3}\right)$

   Step-by-step solution →
5. Q285 CBSE 2023
   Prove ​that ​A$(4,3)$, ​B$(6,4)$, C$(5,6)$, ​D$(3,5)$ are ​the ​vertices of ​a ​square ABCD.
   Show answer

   All sides equal $\sqrt{5}$ and diagonals equal $\sqrt{10}$, so ABCD is a square.

   Step-by-step solution →
6. Q286 CBSE 2023
   Find ​the ratio in ​which $y$-axis ​divides the ​line segment joining ​the points $(5,-6)$ and $(-1,-4)$.
   Show answer

   $5:1$

   Step-by-step solution →
7. Q287 CBSE 2023
   Show that $A(1,2)$, $B(5,4)$, $C(3,8)$ ​and $D(-1,6)$ are ​vertices of ​a ​parallelogram $ABCD$.
   Show answer

   Since the diagonals AC and BD have the same midpoint (2, 5), ABCD is a parallelogram.

   Step-by-step solution →
8. Q288 CBSE 2023
   Show ​that the ​points $A(3,0)$, $B(6,4)$ ​and $C(-1,3)$ are vertices of ​a right-angled ​triangle.
   Show answer

   $A{B}^2+C{A}^2=B{C}^2$ (25 + 25 = 50), so triangle ABC is right-angled at A.

   Step-by-step solution →
9. Q289 CBSE 2023
   Find ​the centre and radius of ​a ​circle having ​end ​points ​of its diameter as $(3,-10)$ and $(1,4)$.
   Show answer

   Centre $(2,-3)$ and radius $5\sqrt{2}$ units.

   Step-by-step solution →
10. Q290 CBSE 2023
    Find the ratio ​in which the point $(-1,k)$ divides the line segment joining ​the ​points $(-3,10)$ and $(6,-8)$. ​Hence, ​find the value of $k$.
    Show answer

    The point divides the segment in the ratio $2:7$, and $k=6$.

    Step-by-step solution →
11. Q291 CBSE 2023
    Find the ratio ​in which ​the ​line ​segment joining the ​points $A(6,3)$ ​and $B(-2,-5)$ is ​divided by $x$-axis.
    Show answer

    The $x$-axis divides AB in the ratio $3:5$

    Step-by-step solution →
12. Q292 CBSE 2023
    Show ​that the ​points $A(1,7)$, $B(4,2)$, $C(-1,-1)$ and $D(-4,4)$ are ​vertices ​of ​the ​square $ABCD$.
    Show answer

    All sides $=\sqrt{34}$ and both diagonals $=\sqrt{68}$, so $ABCD$ is a square.

    Step-by-step solution →
13. Q293 CBSE 2023
    If $(-5,3)$ ​and $(5,3)$ are ​two vertices of an equilateral triangle, then find co-ordinates of ​the third ​vertex, given that ​origin ​lies inside the ​triangle. ​(Take $\sqrt{3}=1.7$)
    Show answer

    The third vertex is $(0,3-5\sqrt{3})=(0,-5.5)$.

    Step-by-step solution →
14. Q294 CBSE 2023
    Find ​a ​relation between $x$ and $y$ such that the point $P(x,y)$ is ​equidistant from ​the ​points $A(0,3)$ ​and $B(-2,1)$.
    Show answer

    The relation is $x+y-1=0$ (equivalently $x+y=1$).

    Step-by-step solution →
15. Q295 CBSE 2023
    If $Q(0,1)$ ​is ​equidistant ​from $P(5,-3)$ ​and $R(x,6)$, ​find ​the values ​of $x$.
    Show answer

    $x=4$ or $x=-4$

    Step-by-step solution →
16. Q296 CBSE 2023
    Find ​the co-ordinates ​of the points of trisection ​of ​the ​line-segment joining the ​points $(5,3)$ and $(4,5)$.
    Show answer

    $P\left(\frac{14}{3},\frac{11}{3}\right)$ and $Q\left(\frac{13}{3},\frac{13}{3}\right)$

    Step-by-step solution →
17. Q297 CBSE 2023
    Determine ​the ratio ​in ​which the point $P(a,-2)$ ​divides the line segment joining ​the points $A(-4,3)$ and $B(2,-4)$. Also, ​find ​the value of ​'$a$'.
    Show answer

    P divides AB in the ratio $5:2$ and $a=\frac{2}{7}$.

    Step-by-step solution →
18. Q298 CBSE 2023
    In ​the given figure, in $△ABC$ points $D$ ​and $E$ ​are mid-points of sides $BC$ ​and $AC$ respectively. ​If given vertices are $A(4,-2)$, $B(2,-2)$ and $C(-6,-7)$, then verify the ​result $DE=\frac{1}{2}AB$.

    Show answer

    $DE=1$ and $AB=2$, so $DE=\frac{1}{2}AB$ is verified.

    Step-by-step solution →
19. Q299 CBSE 2023
    Prove ​that the points $A(-1,0)$, $B(3,1)$, $C(2,2)$ ​and $D(-2,1)$ ​are ​the vertices of a parallelogram ​ABCD. Is ​it also a rectangle ?
    Show answer

    $AB=CD$ and $BC=DA$, so ABCD is a parallelogram; but $AC=\sqrt{13}\ne BD=5$, so it is not a rectangle.

    Step-by-step solution →
20. Q300 CBSE 2023
    Use of mobile screen for long hours makes your eye sight ​weak ​and gives you headaches. Children who are addicted to play "PUBG" can get easily ​stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start ​'BAN PUBG' ​campaign, in which students are asked to prepare campaign board in the shape of a rectangle. One such campaign board ​made ​by class X student ​of the school is shown in the figure, with vertices $A(1,1)$, $B(7,1)$, $C(7,5)$ and $D(1,5)$. Based on the above information, answer the following questions.

    1. (i)Find the coordinates of the point of intersection of diagonals $AC$ and $BD$.[1]
    2. (ii)Find the length of the diagonal $AC$.[1]
    3. (iii)(a)Find the area of the campaign board $ABCD$.[2]
    4. (iii)(b)Find the ratio of the length of side $AB$ to the length of the diagonal $AC$.[2]
    Show answer

    (i) $(4,3)$ (ii) $2\sqrt{13}$ units (iii)(a) $24$ sq units (iii)(b) $3:\sqrt{13}$

    Step-by-step solution →