Question

a triangle on the coordinate plane has points located at a (2, 5), b (5, 9), and c (8, 5). what is the area of the triangle?
a. 24 square units
b. 8 square units
c. 10 square units
d. 12 square units

Explanation:

Step1: Find the base length

The points A(2, 5) and C(8, 5) have the same y - coordinate. The length of the base is the difference in x - coordinates. So, base $b=\vert8 - 2\vert=6$.

Step2: Find the height

The height is the perpendicular distance from the third - point B(5, 9) to the line containing AC. Since the y - coordinate of points on AC is 5 and the y - coordinate of B is 9, the height $h=\vert9 - 5\vert = 4$.

Step3: Calculate the area

Use the triangle area formula $A=\frac{1}{2}bh$. Substitute $b = 6$ and $h = 4$ into the formula: $A=\frac{1}{2}\times6\times4=12$.

Answer:

D. 12 square units