Question

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

विकल्प

• 12

• −2

• −12, −2

• 12, −2

Answer 1

If area of triangle is 35 sq. 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).

Area of Δ = `1/2 |(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

Area of triangle is 35 sq. units.

⇒ `±35 = 1/2|(2,-6,1),(5,4,1),(k,4,1)|`

⇒ `±35 = 1/2 [2|(4,1),(4,1)| + 6|(5,1),(k,1)| + 1|(5,4),(k,4)|]`

⇒ `±35 = 1/2 [2(4 - 4) + 6(5 - k) + 1(20 - 4 k)]`

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

⇒ ±70 = 6(5 − k) + 20 − 4k

⇒ ±70 = 30 − 6k + 20 − 4k

⇒ ±70 = 50 − 10k

⇒ ±7 = 5 − k

⇒ 7 = 5 − k or −7 = 5 − k

⇒ k = 5 − 7 or k = 5 + 7

k = −2 or k = 12

∴ k = 12, −2