Question

Using determinants, find the area of ΔPQR with vertices P(3, 1), Q(9, 3) and R(5, 7). Also, find the equation of line PQ using determinants.

Answer 1

Given vertices of triangle ΔPQR are P(3, 1), Q(9, 3) and R(5, 7).

Area of ΔPQR = `1/2 |(3, 1, 1),(9, 3, 1),(5, 7, 1)|`

= `1/2 {3(3 - 7) - (9 - 5) + (63 - 15)}`

= `1/2 {-12 - 4 + 48}`

= `1/2 xx 32`

= 16 sq. units.