If the vertices of LABC be A(1, –3), B(4, p) and C(–9, 7) and its area is 15 square units, find the values of p.

Question

Philoid · Accepted Answer

Area = 15

⇒ Δ = 1/2(x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂))

15 = 1/2(x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂))

15 = 1/2(1(p–7) + 4(7 + 3)–9(–3–p))

15 = 1/2(10p + 16)

|10p + 16| = 30

10p + 16 = 30 or –30

Hence, p = −9 or p = −3.