Question

Find the area of the triangle with coordinates A(-2, 1), B(3, 3) and C(1, -2).

• A. 10 sq. units
• B. 10.5 sq. units
• C. 11 sq. units
• D. 11.5 sq. units

Answer 1

The correct option is B

10.5 sq. units

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

Given, ($x_1,y_1$) = (-2, 1)

($x_2,y_2$) = (3, 3)

($x_3,y_3$) = (1, -2)

$=\frac{1}{2}[-2(3+2)+3(-2-1)+1(1-3\left)\right]=-10.5$

Since area is not a negative quantity, take the absolute value.

Thus, area of the given triangle = 10.5 sq. units.