Question

Find values of k if area of triangle is 4 sq. units and vertices are (k, 0), (4, 0), (0, 2).

Answer 1

Area of triangle = 4 sq. units

Again, area of triangle = `1/2 |(k,0,1),(4,0,1),(0,2,1)|`

= `1/2 [k|(0,1),(2,1)| - 0|(4,1),(0,1)| + 1|(4,0),(0,2)|]`

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

= `1/2 [-2k + 8]`

= −k + 4

Now, −k + 4 = ±4

⇒ −k + 4 = 4 or −k + 4 = −4

⇒ k = 0 or k = 8

⇒ k = 0, 8