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. 8 square units
b. 10 square units
c. 24 square units
d. 12 square units

Explanation:

Step1: Identify base and height

The points A(2, 5) and C(8, 5) have the same y - coordinate. The distance between them is the base of the triangle. Using the distance formula for points with the same y - coordinate $d=\vert x_2 - x_1\vert$, we have $b=\vert8 - 2\vert=6$. The height is the perpendicular distance from point B(5, 9) to the line segment AC. Since the y - coordinate of points on AC is 5, the height $h=\vert9 - 5\vert = 4$.

Step2: Apply area formula

The area of a triangle is given by the formula $A=\frac{1}{2}bh$. Substitute $b = 6$ and $h = 4$ into the formula: $A=\frac{1}{2}\times6\times4$.
$A = 12$.

Answer:

12 square units