Chapter 7 · Coordinate Geometry

NCERT Exemplar Class 10 Maths Exercise 7.2

All 12 questions of NCERT Exemplar Class 10 Maths Exercise 7.2 (Coordinate Geometry), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   $△ABC$ 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 $(0,4)$.
   Show answer

   True

   Step-by-step solution →
2. Q2
   Point $P(-4,2)$ ​lies on ​the ​line ​segment joining the ​points $A(-4,6)$ and $B(-4,-6)$.
   Show answer

   True

   Step-by-step solution →
3. Q3
   The ​points $(0,5)$, $(0,-9)$ ​and $(3,6)$ ​are ​collinear.
   Show answer

   False

   Step-by-step solution →
4. Q4
   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 $B(3,3)$.
   Show answer

   False

   Step-by-step solution →
5. Q5
   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

   Step-by-step solution →
6. Q6
   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.
   Show answer

   False

   Step-by-step solution →
7. Q7
   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

   Step-by-step solution →
8. Q8
   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

   Step-by-step solution →
9. Q9
   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

   Step-by-step solution →
10. Q10
    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

    Step-by-step solution →
11. Q11
    The ​point $P(-2,4)$ lies ​on ​a ​circle of radius 6 ​and ​centre $C(3,5)$.
    Show answer

    False

    Step-by-step solution →
12. Q12
    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.
    Show answer

    True

    Step-by-step solution →