Q) 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

(ii) (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)?

Ans:

(i) Co-ordinates of R and S:

Given that the coordinates of P are (-200, 0) and of Q are (200, 0).

Therefore, PQ = 400

Since, PQRS is a square, therefore, PQ = PS = RS = QR = 400

Hence, coordinates of R are (200,400) and of S are (-200,400)

(ii) (a) Area of square:

We know that, Area of square = side2

We just calculated that side PQ = 400 Area = (400)2

= 160,000 sq. units

Therefore, area of square PQRS is 160,000 sq. units.

(ii) (b) Length of diagonal PR:

In Square PQRS, PR2 = (400)2 + (400)2 = 320000

PR = 400 √2 units

(iii) Value of K:

Given that the coordinates of point A are (200, 800)

By graph, we can note that the coordinates of point C are (-600, 0).

Coordinates of S we already have as (-200,400)

By using section formula for internal division, we get coordinates of S:

-200 =  K = 1

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