Question

the graph shows the vertices of a triangle. determine the area of the triangle. enter the unknown segment length(s), then calculate the area of the polygon. area of the triangle: 33 square units

Explanation:

Step1: Identify base and height

The base of the triangle can be found between points \(O(1, - 3)\) and \(I(7,-3)\). The length of the base \(b\) is calculated using the distance formula for two - points on a horizontal line (\(y\) - coordinates are the same): \(b=\vert x_2 - x_1\vert=\vert7 - 1\vert = 6\). The height \(h\) of the triangle is the vertical distance from the point \(H(1,8)\) to the line \(y=-3\). So \(h=\vert8-(-3)\vert=11\).

Step2: Apply area formula

The area formula for a triangle is \(A=\frac{1}{2}bh\). Substitute \(b = 6\) and \(h = 11\) into the formula: \(A=\frac{1}{2}\times6\times11\).

$$A = 33$$

Answer:

33 square units