Question

plot and connect the points listed below. when you are done, find the area of the triangle. a(1, -1), b(3, 2), c(5, -1) 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: Find the base length

Points A(1, -1) and C(5, -1) have the same y - coordinate, so the distance between them (the base of the triangle) is calculated by the formula for the distance between two points with the same y - coordinate: \(d=\vert x_2 - x_1\vert\). Here, \(x_1 = 1\), \(x_2=5\), so the base \(b=\vert5 - 1\vert=4\).

Step2: Find the height

The height of the triangle is the vertical distance from point B(3, 2) to the line AC (since AC is horizontal). The y - coordinate of points on AC is - 1, and the y - coordinate of B is 2. So the height \(h=\vert2-(-1)\vert = 3\).

Step3: Calculate the area

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Substituting \(b = 4\) and \(h = 3\) into the formula, we get \(A=\frac{1}{2}\times4\times3\).
First, \(\frac{1}{2}\times4 = 2\), then \(2\times3=6\).

Answer:

6