Question

plot and connect the points listed below. when you are done, find the area of the triangle.
a(-1, 4), b(3, 4), c(1, 0)
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 length of AB

Points A(-1, 4) and B(3, 4) have the same y - coordinate. The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(y_1=y_2 = 4\), the length of AB is \(|3-(-1)|=|3 + 1|=4\).

Step2: Find the height from C to AB

The line AB is horizontal (since \(y\) - coordinate is constant). The height from point C(1, 0) to the line AB (where \(y = 4\)) is the vertical distance between \(y = 0\) and \(y=4\), which is \(|4 - 0| = 4\).

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is the length of AB (\(b = 4\)) and the height is the vertical distance from C to AB (\(h = 4\)). So \(A=\frac{1}{2}\times4\times4 = 8\).

Answer:

The area of the triangle is 8.