Question

triangle pqr is an isosceles triangle with the coordinates p(2, 3), q(5, 10), and r(8, 3). what is the area of triangle pqr? a. 15 units² b. 21 units² c. 30 units² d. 42 units² e. 65 units²

Explanation:

Step1: Identify base length

Points $P(2,3)$ and $R(8,3)$ have the same $y$-coordinate, so the length of $PR$ is the difference in $x$-coordinates:
$PR = 8 - 2 = 6$ units

Step2: Find height of the triangle

The height is the vertical distance from $Q(5,10)$ to the line $PR$ (which is $y=3$):
$\text{Height} = 10 - 3 = 7$ units

Step3: Calculate triangle area

Use the area formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$:
$\text{Area} = \frac{1}{2} \times 6 \times 7 = 21$

Answer:

B. 21 units²