Chapter 7 · Coordinate Geometry

NCERT Class 10 Maths Exercise 7.2

All 10 questions of NCERT 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
   Find the coordinates of the ​point which ​divides ​the join ​of $(-1,7)$ ​and $(4,-3)$ in the ​ratio $2:3$.
   Show answer

   $P=(1,3)$

   Step-by-step solution →
2. Q2
   Find the coordinates ​of ​the ​points of ​trisection of the ​line segment ​joining (4, -1) and (-2, -3).
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   Trisection points: $P=\left(2,-\frac{5}{3}\right)$ and $Q=\left(0,-\frac{7}{3}\right)$.

   Step-by-step solution →
3. Q3
   To conduct ​Sports Day activities, in your rectangular shaped ​school ground ABCD, lines have ​been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as ​shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth ​line ​and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line ​segment joining the two ​flags, where should she post her flag?

   Show answer

   Distance between green and red flags $=\sqrt{61}\approx 7.81$ m; blue flag at $(5,22.5)$ — on the 5th line, $22.5$ m from $A$.

   Step-by-step solution →
4. Q4
   Find ​the ratio ​in ​which the line segment joining ​the points $(-3,10)$ ​and $(6,-8)$ is ​divided by $(-1,6)$.
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   Ratio $=2:7$ (internal division).

   Step-by-step solution →
5. Q5
   Find ​the ​ratio in ​which the line ​segment joining $A(1,-5)$ and $B(-4,5)$ is divided by the $x$-axis. Also find the coordinates of the point of ​division.
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   Ratio $=1:1$; point of division $P=\left(-\frac{3}{2},0\right)$.

   Step-by-step solution →
6. Q6
   If $(1,2),(4,y),(x,6)$ and $(3,5)$ are ​the ​vertices ​of a ​parallelogram taken ​in order, ​find $x$ ​and $y$.
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   $x=6$ and $y=3$.

   Step-by-step solution →
7. Q7
   Find ​the coordinates of ​a point $A$, where $AB$ is ​the diameter of ​a circle ​whose centre is $(2,-3)$ and $B$ is $(1,4)$.
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   $A=(3,-10)$.

   Step-by-step solution →
8. Q8
   If $A$ ​and $B$ are $(-2,-2)$ and $(2,-4)$ respectively, find the ​coordinates ​of $P$ such that $AP=\frac{3}{7}AB$ and $P$ lies on the line segment $AB$.
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   $P=\left(-\frac{2}{7},-\frac{20}{7}\right)$.

   Step-by-step solution →
9. Q9
   Find ​the coordinates ​of ​the points which divide the line segment joining A(-2, ​2) and ​B(2, 8) into four ​equal parts.
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   $P_1=\left(-1,\frac{7}{2}\right),P_2=(0,5),P_3=\left(1,\frac{13}{2}\right)$.

   Step-by-step solution →
10. Q10
    Find ​the area ​of ​a rhombus ​if its ​vertices are ​(3, 0), (4, 5), ​(-1, 4) and (-2, -1) taken in order. [Hint: ​Area of a rhombus = $\frac{1}{2}$ (product of its diagonals)]
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    Area $=24$ square units.

    Step-by-step solution →