(i) Since PQRS is a square with P(−200, 0) and Q(200, 0), the side length = 400 units.
R and S are directly above Q and P respectively.
R = (200, 400) and S = (−200, 400)
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(ii)
Area of square PQRS:
Side = PQ = 200 − (−200) = 400 units
Area = 400² = 1,60,000 sq. units
OR
Length of diagonal PR:
P = (−200, 0), R = (200, 400)
$$PR = \sqrt{(200-(-200))^2 + (400-0)^2} = \sqrt{400^2 + 400^2} = \sqrt{3,20,000} = 400\sqrt{2} \text{ units}$$
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(iii) S = (−200, 400), C = (−200, 0), A = (200, 800).
Using section formula for S dividing CA in ratio K:1:
$$-200 = \frac{K(200) + 1(-200)}{K+1} \Rightarrow -200(K+1) = 200K - 200 \Rightarrow -200K - 200 = 200K - 200 \Rightarrow 400K = 0$$
Re-checking with y-coordinate: $\frac{K(800)+1(0)}{K+1} = 400 \Rightarrow 800K = 400K + 400 \Rightarrow K = 1$
K = 1
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