Question

In a square there are equations of 2 sides `5x-12y-65=0` and `5x-12y+26=0`.How to calculate the area of the square, using determinants?

Answer 1

`49" sq. unit."`

Explanation:

Prerequisites :

The Distance between parallel lines :

`ax+by+c=0, &, ax+by+c'=0` is given by, `|c-c'|/sqrt(a^2+b^2)`.

Observe that the given eqns. represent parallel lines. So, they

are the eqns. of the opposite lines of the square.

Clearly, the `bot-` distance between them is the length of

a side of a `square.`

This distance is, `|26-(-65)|/sqrt(5^2+(-12)^2)=(26+65)/13=7`.

Hence, the reqd. Area of the `square` is `7^2=49" sq. unit"`.