Question

Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to ______.

पर्याय

• `|m + n|/(m - n)^2`

• `2/|m + n|`

• `1/|m + n|`

• `1/|m - n|`

Answer 1

Area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 is equal to `underlinebb(1/|m + n|)`.

Explanation:

Let lines,

OB `\implies` y = mx

CA `\implies` y = mx + 1

BA `\implies` y = – nx + 1

and OC `\implies` y = – nx

The point of intersection B of OB and AB has x-coordinates `1/(m + n)`

Now, area of a parallelogram OBAC

= 2 × area of ΔOBA

= `2 xx 1/2 xx OA xx DB`

= `2 xx 1/2 xx 1/(m + n)`

= `1/(m + n)`

= `1/|m + n|`