Question

find the value of k, if the area of a triangle formed by the points (2,4),(5,k) and (3,10) is 15 sq units.

Answer 1

If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the vertices of a triangle then its area is given by / 2 [x₁(y₂ - y₃) + x₂( y₃ - y₁)+ x₃(y₁ - y₂)] square units.

Given the vertices of a triangle are (2,4),(5,k) and (3,10) and its area is 15 sq .units.

⇒ 15 = 1/2 [2(k - 10) + 5( 10 - 4) + 3(4 - k)]

30 = 2k - 20 + 30 +12 - 3k

-k +22 = 30

-k =30-22

-k =8

=>k =-8

∴ k = -8.