Class 10 Maths · Chapter 7

Coordinate Geometry

112 Class 10 Maths questions on Coordinate Geometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 3 of 6

1. Q41 Exemplar · Exercise 7.2
   $△ABC$ with vertices A $(-2,0)$, ​B $(2,0)$ ​and C $(0,2)$ is ​similar ​to $△DEF$ with ​vertices ​D $(-4,0)$, ​E $(4,0)$ and F $(0,4)$.
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   True

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2. Q42 Exemplar · Exercise 7.2
   Point $P(-4,2)$ ​lies on ​the ​line ​segment joining the ​points $A(-4,6)$ and $B(-4,-6)$.
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   True

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3. Q43 Exemplar · Exercise 7.2
   The ​points $(0,5)$, $(0,-9)$ ​and $(3,6)$ ​are ​collinear.
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   False

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4. Q44 Exemplar · Exercise 7.2
   Point $P(0,2)$ is ​the point ​of ​intersection ​of ​the $y$-axis ​and perpendicular bisector of the line ​segment joining ​the points $A(-1,1)$ and $B(3,3)$.
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   False

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5. Q45 Exemplar · Exercise 7.2
   State whether the following ​statement is ​true or ​false and justify: Points ​A $(3,1)$, ​B $(12,-2)$ and C $(0,2)$ cannot be the vertices of a triangle.
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   True

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6. Q46 Exemplar · Exercise 7.2
   Points ​A $(4,3)$, B $(6,4)$, C $(5,-6)$ and D $(-3,5)$ are the vertices ​of a parallelogram. ​State ​whether this statement ​is ​true or ​false, and justify your answer.
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   False

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7. Q47 Exemplar · Exercise 7.2
   A ​circle ​has its centre at the origin and a point $P(5,0)$ lies ​on ​it. The ​point $Q(6,8)$ lies outside the ​circle.
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   True

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8. Q48 Exemplar · Exercise 7.2
   The ​point ​A $(2,7)$ ​lies on the perpendicular bisector ​of ​line segment joining the points P $(6,5)$ and ​Q $(0,-4)$.
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   False

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9. Q49 Exemplar · Exercise 7.2
   Point $P(5,-3)$ ​is ​one of the ​two points of trisection ​of the line ​segment joining the ​points $A(7,-2)$ and $B(1,-5)$.
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   True

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10. Q50 Exemplar · Exercise 7.2
    Points ​A $(-6,10)$, ​B $(-4,6)$ ​and ​C $(3,-8)$ ​are collinear such that $AB=\frac{2}{9}AC$.
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    True

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11. Q51 Exemplar · Exercise 7.2
    The ​point $P(-2,4)$ lies ​on ​a ​circle of radius 6 ​and ​centre $C(3,5)$.
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    False

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12. Q52 Exemplar · Exercise 7.2
    State whether the following is ​true or ​false ​and ​justify: The points $A(-1,-2)$, $B(4,3)$, $C(2,5)$ ​and $D(-3,0)$ in that order form ​a ​rectangle.
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    True

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13. Q53 Exemplar · Exercise 7.3
    Find ​the ​ratio ​in which the point $P\left(\frac{3}{4},\frac{5}{12}\right)$ divides ​the line segment joining the points $A\left(\frac{1}{2},\frac{3}{2}\right)$ and $B(2,-5)$.
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    $P$ divides $AB$ in the ratio $1:5$ (from $A$ to $B$).

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14. Q54 Exemplar · Exercise 7.3
    Name ​the type ​of ​triangle ​formed by ​the points $A(-5,6)$, $B(-4,-2)$ and $C(7,5)$.
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    All three sides are unequal and no Pythagorean relation holds, so $△ABC$ is a scalene triangle (and not right-angled).

    Step-by-step solution →
15. Q55 Exemplar · Exercise 7.3
    Find the ​points ​on the $x$-axis ​which ​are at a distance of $2\sqrt{5}$ from the point $(7,-4)$. ​How ​many ​such ​points are there?
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    The points are (9, 0) and (5, 0). There are two such points.

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16. Q56 Exemplar · Exercise 7.3
    What type ​of ​a quadrilateral do ​the points $A(2,-2)$, $B(7,3)$, $C(11,-1)$ ​and $D(6,-6)$ taken in ​that ​order, ​form?
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    $ABCD$ is a rectangle: opposite sides $AB=CD=5\sqrt{2}$ and $BC=DA=4\sqrt{2}$, diagonals $AC=BD=\sqrt{82}$; the adjacent sides are unequal, so it is not a square.

    Step-by-step solution →
17. Q57 Exemplar · Exercise 7.3
    Find ​the value of $a$, if ​the distance ​between the ​points $A(-3,-14)$ and $B(a,-5)$ is $9$ ​units.
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    $a=-3$.

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18. Q58 Exemplar · Exercise 7.3
    Find a ​point which ​is ​equidistant ​from the ​points $A(-5,4)$ and $B(-1,6)$. ​How ​many such points are there?
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    $(-3,5)$ is one such point (the midpoint of $AB$); there are infinitely many, all lying on the perpendicular bisector of $AB$.

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19. Q59 Exemplar · Exercise 7.3
    Find ​the coordinates of the point $Q$ on the $x$-axis which lies on the perpendicular bisector of ​the line ​segment joining the points $A(-5,-2)$ and $B(4,-2)$. Name the ​type ​of triangle formed by ​the ​points $Q$, $A$ and $B$.
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    $Q=\left(-\frac{1}{2},0\right)$; triangle $QAB$ is isosceles since $QA=QB$.

    Step-by-step solution →
20. Q60 Exemplar · Exercise 7.3
    Find the ​value ​of $m$ ​if ​the ​points $(5,1)$, $(-2,-3)$ and $(8,2m)$ are ​collinear.
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    $m=\frac{19}{14}$

    Step-by-step solution →