Question

What is the area of triangle ABC?

Answer 1

Answer:

7 square units

Step-by-step explanation:

As you can observe in the image attached, we know the coordinates of each vertex of the triangle.

To find the area using only its vertex coordinates, we need to use the following formula

$A=\frac{1}{2}[x_{1}(y_{2} -y_{3}+x_{2}(y_{3} -y_{1} )+x_{3}(y_{1}-y_{2} ) )$

Where the coordinates are

$A(1,1)\\B(4,0)\\C(3,5)$

Replacing coordinates, we have

$A=\frac{1}{2}[1(0 -5)+4(5 -1 )+3(1-0 ) ]\\A=\frac{1}{2} [-5+16+3]=\frac{1}{2}(14)\\ A=7$

Therefore, the area of the triangle is 7 square units. So, the right answer is the second choice.