Question

Find the value of k, if area of ΔPQR is 4 square units and vertices are P(k, 0), Q(4, 0), R(0, 2).

Answer 1

Here, P(x₁, y₁) ≡ P(k, 0), Q(x₂, y₂) ≡ Q(4, 0), R(x₃, y₃) ≡ R(0, 2)
A(ΔPQR) = 4 sq. units

Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y3, 1)|`

∴ ± 4 = `1/2|("k", 0, 1),(4, 0, 1),(0, 2, 1)|`

∴ ± 4 = `1/2["k"(0 - 2) - 0 + 1 (8 - 0)]`

∴ ± 8 = –2k + 8
∴ 8 = –2k + 8 or –8 = –2k + 8
∴ –2k = 0       or 2k = 16
∴ k = 0           or  k = 8