Question

If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4), then k is ______.

Options

• 12

• -2

• −12, −2

• 12, −2

Answer 1

If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4). Then k is 12, −2.

Explanation:

Given, the vertices of the triangle are (2, -6), (5, 4) and (k, 4);

`Delta` Area of = `Delta = 1/2 abs ((x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1))`

x₁ = 2, y₁ = 6, x₂ = 5, y₂ = 4, x₃ = k, y₃ = 4

`Delta` Area of  `pm 35`

`pm 35 = 1/2 [2(4 - 4) + 6(5 - k) + k (120 - 4 k)`

`=> pm 35 = 1/2 [ 2 xx 0 + 6(5 - k) + 1 (20 - 4 k)]`

`=> pm 70 = 6(5 - k) + 20 - 4 k`

`=> pm 70 = 30 - 6 k + 20 - 4 k`

`=> pm 70 = 50 - 10 k`

`=> pm 70 = 5 - k`

7 = 5 - k

⇒ k = 5 - 7

k = -2

-7 = 5 - k

⇒ - 12 = - k

⇒ k = 12

अत: k = 12, -2