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?

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Answer 1 · 2018-01-08T10:17:24

# 49" sq. unit."#

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"#.