Question

plot and connect the points listed below. when you are done, find the area of the triangle.
a(-5, 0), b(3, -2), c(-5, -4)
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 the base and height

Points \( A(-5,0) \) and \( C(-5,-4) \) have the same \( x \)-coordinate, so the distance between them (the length of \( AC \)) is the vertical distance. The formula for vertical distance is \( |y_2 - y_1| \). So, \( AC = |0 - (-4)| = 4 \).

Points \( A(-5,0) \) and \( C(-5,-4) \) form a vertical line, and the horizontal distance from this line to point \( B(3,-2) \) is the horizontal distance between \( x = -5 \) and \( x = 3 \), which is \( |3 - (-5)| = 8 \). This horizontal distance is the height of the triangle with base \( AC \).

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Substituting the values of base (\( AC = 4 \)) and height (\( 8 \)) into the formula:

$$ \text{Area} = \frac{1}{2} \times 4 \times 8 $$

$$ \text{Area} = 2 \times 8 = 16 $$

Answer:

The area of the triangle is \( 16 \).