Question

Find area of triangle whose vertices are (1, 1), (2, 3) and (4, 5)

• A. 1 sq unit.
• B. 2 sq units.
• C. 3 sq units.
• D. 4 sq units.

Answer 1

The correct option is A 1 sq unit.

We have
$(x_1,y_1)=(1,1)$
$(x_2,y_2)=(2,3)$ and
$(x_3,y_3)=(4,5)$

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

$=\frac{1}{2}\left[1\right(3-5)+2(5-1)+4(1-3\left)\right]=\frac{1}{2}(-2+8-8)=\frac{1}{2}(-2)=-1$

Area cannot be negative. We only consider the numerical value of answer.
Therefore, area of triangle = 1 sq units