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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.
Solution
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.
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