Question

plot and connect the points listed below. when you are done, find the area of the triangle.
a(2, -5), b(5, 2), c(5, -5)
click on the graph to plot a point. click a point to delete it.
when you are done, press \graph figure\ to see the result.

Explanation:

Step1: Identify base and height

Points \( A(2, -5) \), \( C(5, -5) \) have the same \( y \)-coordinate, so \( AC \) is horizontal. Length of \( AC \): \( |5 - 2| = 3 \). Points \( B(5, 2) \), \( C(5, -5) \) have the same \( x \)-coordinate, so \( BC \) is vertical. Length of \( BC \): \( |2 - (-5)| = 7 \).

Step2: Calculate area of triangle

Area of triangle \( = \frac{1}{2} \times \text{base} \times \text{height} \). Here, base \( = AC = 3 \), height \( = BC = 7 \). So area \( = \frac{1}{2} \times 3 \times 7 = \frac{21}{2} = 10.5 \).

Answer:

\( 10.5 \) (or \( \frac{21}{2} \))