Question

Find the value of k, if area of ΔLMN is `33/2` square units and vertices are L(3, − 5), M(− 2, k), N(1, 4).

Answer 1

Here, L(x₁, y₁) ≡ L(3, − 5), M(x₂, y₂) ≡ M(− 2, k), N(x₃, y₃) ≡ N(1, 4)

A(ΔLMN ) = `33/2` q. units

Area of a triangle = `1/2|(x_1, y_1, 1),(x2, y_2, 1),(x3, y_3, 1)|`

∴ `± 33/2 = 1/2|(3, -5, 1),(-2, "k", 1),(1, 4, 1)|`

∴ `± 33/2 = 1/2[3("k" - 4) - (-5) (-2 - 1) + 1 (-8 - k)]`
∴ ± 33 = 3k – 12 – 5 – 8 – k
∴ ± 33 = 2k – 35
∴ 2k – 35 = 33   or 2k – 35 = –33
∴ 2k  = 68         or 2k = 2
∴ k = 34            or k = 1