Question

Given three vertices of a triangle whose coordinates are A (1, 1), B (3, -3) and (5, -3). Find the area of the triangle.

• A. 3 square units
• B. 4 square units
• C. 5 square units
• D. 6 square units

Answer 1

The correct option is B 4 square units

We know that the area of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

The three vertices of the triangle are $A(1,1),B(3,-3),C(5,-3)$

Area of triangle $=\frac{|1(-3-(-3)+3(-3-1)+5(1-(-3))|}{2}$

$=\frac{|1\left(0\right)+3(-4)+4\left(4\right)|}{2}$

$=\frac{|-12+20|}{2}$

$=\frac{8}{2}$

$=4$ square units.