Question

Find the area of triangle FGH with coordinates F(-6,1), G(-5,-4), and H(2,1). Which of the following is the correct area?

A. 21.7 square units
B. 10 square units
C. 20 square units
D. 40 square units

Answer 1

Using the coordinates of triangle FGH and the formula for the area of a triangle in a coordinate plane, the area is calculated to be 20 square units. The correct answer is C. 20 square units.

Step-by-step explanation:

To calculate the area of triangle FGH, you can use the formula for the area of a triangle with points in a coordinate plane, which is ½ |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.

Let's apply this formula to the given coordinates:

• F(-6,1)
• G(-5,-4)
• H(2,1)

Using these coordinates:

Area = ½ |-6(-4-1) + -5(1-1) + 2(1+4)|

Area = ½ |(-6)(-5) + 0 + 2(5)|

Area = ½ |30 + 10|

Area = ½ |40|

Area = 20 square units

Therefore, the correct answer is C. 20 square units.