Case Study -3 Trees act the natural filters. By planting trees in and around school premises, we create cleaner and…
CBSE Class 10 Maths PYQ · Coordinate Geometry · Application · 4 Marks · July 2025 · Standard
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1324 Marks · July 2025 · Standard
Case Study -3 Trees act the natural filters. By planting trees in and around school premises, we create cleaner and healthier air for students and local residents, reducing respiratory problems. A school in Noida has proposed and organised a community drive on tree plantation under the title "Save Earth, Plant Trees". Students of that school have planted saplings in the field such that it formed a quadrilateral as shown in the figure ABCD. Based on the information given above, answer the following questions : (i) Find the distance between the two saplings at A and D. (ii) (a) One student plants one sapling at the mid-point of AD. Then he moves along a straight line parallel to DB and sows another sapling on AB. What are the coordinates of the positions of these two new saplings? OR (ii) (b) A new sapling is kept at a point M on DB such that DM : MB = $3:1$. Find the coordinates of M. (iii) The line segments AC and BD bisect each other at P$(-2, 2)$. Find the coordinates of C.
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(i) Observing the graph, coordinators of points are A $(-5, 9)$ and D $(-6, 1)$ AD = $\sqrt{(-6 + 5)^2 + (1 - 9)^2} = \sqrt{65}$ (ii) (a) Mid point of AD = $\left(\frac{-6-5}{2}, \frac{1+9}{2}\right)$ i.e. $\left(-\frac{11}{2}, 5\right)$ Student will sow another sapling at mid point of AB. Point B is $(2, 3)$ Mid point of AB = $\left(\frac{2-5}{2}, \frac{3+9}{2}\right)$ i.e. $\left(-\frac{3}{2}, 6\right)$ OR (b) Coordinates of M = $\left(\frac{3 \times 2 + 1 \times (-6)}{3+1}, \frac{3 \times 3 + 1 \times 1}{3+1}\right)$ i.e. $\left(0, \frac{5}{2}\right)$ (iii) Coordinates of C are $(1, -5)$
