Question

plot and connect the points listed below. when you are done, find the area of the triangle.
a(-3,1), b(5,1), c(-3,-3)
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: Determine the base length

Points A(-3,1) and B(5,1) have the same y - coordinate, so the distance between them (the base of the triangle) is the absolute difference of the x - coordinates.
The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\) is \(d=\vert x_2 - x_1\vert\).
For points A and B, \(x_1=-3\), \(x_2 = 5\), so the base \(b=\vert5-(-3)\vert=\vert5 + 3\vert=8\).

Step2: Determine the height length

Points A(-3,1) and C(-3,-3) have the same x - coordinate, so the distance between them (the height of the triangle) is the absolute difference of the y - coordinates.
The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1=x_2\) is \(d=\vert y_2 - y_1\vert\).
For points A and C, \(y_1 = 1\), \(y_2=-3\), so the height \(h=\vert-3 - 1\vert=\vert-4\vert = 4\).

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).
Substitute \(b = 8\) and \(h = 4\) into the formula: \(A=\frac{1}{2}\times8\times4\).
First, \(\frac{1}{2}\times8 = 4\), then \(4\times4=16\).

Answer:

16