Question

If the 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

12, – 2

Explanation:

The area of the triangle with vertices (2, – 6), (5, 4) and (k, 4) is given by the relation.

Δ = `1/2|(2, -6, 1),(5, 4, 1),(k, 4, 1)|`

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

= `1/2[30 - 6k + 20 - 4k]`

= `1/2[50 - 10k]`

= `25 - 5k`

Given, the area of the triangle is ± 35.

Thus, we have:-

⇒ `2^5 - 5k = +- 35`

⇒ `5(5 - k) = +- 35`

⇒ `5 - k = +- 7`

When `5 - k = - 7, k = 5 + 7 = 12`

When `5 - k = - 7, k = 5 - 7 = - 2`

Therefore, `k = 12, -2`.