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Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O.
Based on the above information, answer the following questions :
(i) Taking O as origin, coordinates of P are $(-200, 0)$ and of Q are $(200, 0)$. PQRS being a square, what are the coordinates of R and S? (ii) (a) What is the area of square PQRS ?
OR
(b) What is the length of diagonal PR in square PQRS ?
(iii) If S divides CA in the ratio K:1, what is the value of K, where point A is $(200, 800)$ ?
Based on the above information, answer the following questions :
(i) Taking O as origin, coordinates of P are $(-200, 0)$ and of Q are $(200, 0)$. PQRS being a square, what are the coordinates of R and S? (ii) (a) What is the area of square PQRS ?
OR
(b) What is the length of diagonal PR in square PQRS ?
(iii) If S divides CA in the ratio K:1, what is the value of K, where point A is $(200, 800)$ ?
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Sol. (i) R$(200, 400)$, S$(-200, 400)$(ii) (a) side PQ = $(200+200)$ m = $400$ m
Area of square PQRS = $400 \times 400$
$= 160000$ sq. units
OR
(ii) (b) Diagonal PR = $\sqrt{(400)^2 + (400)^2}$
$= \sqrt{3200}$ or $400\sqrt{2}$
(iii) C$(-600,0)$; A$(200,800)$; S$(-200,400)$
S divides CA in the ratio k: $1$
$-200 = \frac{k(200)+1(-600)}{k+1}$
$\Rightarrow k = 1$
Area of square PQRS = $400 \times 400$
$= 160000$ sq. units
OR
(ii) (b) Diagonal PR = $\sqrt{(400)^2 + (400)^2}$
$= \sqrt{3200}$ or $400\sqrt{2}$
(iii) C$(-600,0)$; A$(200,800)$; S$(-200,400)$
S divides CA in the ratio k: $1$
$-200 = \frac{k(200)+1(-600)}{k+1}$
$\Rightarrow k = 1$