Question

The area of  ΔABC whose vertices are A (x,2), B(2x,6), C(x,5) is 6, then what will be the value of x?

1. 4
2. 5
3. 6
4. 7

Answer 1

Correct Answer - Option 1 : 4

As per Coordinate Geometry, the area of a triangle with vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃)  is given by:

\(A =\frac{1}{2}[x_1(y_2-y_3) +x_2(y_3-y_1) +x_3(y_1-y_2)]\)

Putting values in the equation gives 

\(A=\frac{1}{2}[x(6-5)+2x(5-2)+x(2-6)]\)

\(A=\frac{\large3\large x}{\large2}\)

Given that area of the Δ is 6.

\(\therefore \frac{\large 3 \large x}{\large 2}=6\)

\(\therefore x=4\)