Question

The area of parallelogram whose two sides are y = x + 3, 2x – y = 0 and remaining two sides are passing through (0, 0) is

(a) 2 sq unit 

(b) 3 sq unit

(c) (5/2) sq unit

(d) (7/2) sq unit

Answer 1

The correct option (b) 3 sq unit

Explanation:

sides are y = x + 3 and 2x – y + 1 = 0

The parallelogram can be drawn as shown.

∴ other side of parallelogram will have slope same as that of y = x + 3

i.e. m = 1. eqn of it is (y – 0) = 1(x – 0) i.e. x – y = 0

Now AP = [(|3|)/√(1 + 1)] = (3/√2)

Line CD and AD intersect in point D given by (– 1, 1)

∴ CD = √(1 + 1) = √2

∴ area of parallelogram = AP × CD = (3/√2) × √2 = 3 sq units.