Question

The area of the triangle formed by the points (5,2), (4,7) and (7,-4) is sq.units.

• A. 2
• B. 3
• C. 4

Answer 1

The correct option is A 2

If A$(x_1,y_1)$ B$(x_2,y_2)$ , C$(x_3,y_3)$ are the vertices of triangle ABC, then its area is given by

Area of triangle = $\frac{1}{2}\left[x_1\right(y_2-y_1)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

Substituting the value of $(x_1,y_1)(x_2,y_2)$ and $(x_3,y_3)$, we get

= $\frac{1}{2}\left[5\right(7+4)+4(-4-2)+7(2-7\left)\right]$

= $\frac{1}{2}[55-24-35]=-\frac{4}{2}=-2$

Since area is a measure, which cannot be negative, we will take the numerical value of -2

Therefore, the area of the triangle is 2 square units.