Co-ordinate Geometry for what value of a the area of triangle formed by the points (2, 4), (6. a) and
|-1, 1) is 9 sq. units?

The value of a  = 14

Step-by-step explanation:

Given

(x₁, y₁) = (2, 4)

(x₂, y₂) = (6, a)

(x₃, y₃) = (-1, 1)

A = 9 sq.units

Area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

substituting the values (x₁, y₁) = (2, 4), (x₂, y₂) = (6, a), (x₃, y₃) = (-1, 1), A = 9 in th formula

Multiply both sides by 2

simplify

As the area is always positive.

so

Add 18 to both sides

simplify

Divide both sides by 3

Thus, the value of a  = 14