Question

the vertices of a triangle are listed below. l(2, 2), m(6, -2), n(2, -6) what is the area of the triangle? a. 16 square units b. 8 square units c. 19.3 square units d. 32 square units

Explanation:

Step1: Calculate the length of the vertical side (base)

The points \(L(2,2)\) and \(N(2, - 6)\) have the same \(x\) - coordinate. Using the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) \(d=\vert y_2 - y_1\vert\) (since \(x_1=x_2\)), we get \(LN=\vert-6 - 2\vert=\vert-8\vert = 8\).

Step2: Calculate the horizontal distance (height)

The points \(L(2,2)\) and \(M(6,-2)\). The horizontal distance (since the base \(LN\) is vertical, the height is the horizontal distance from \(M\) to the line \(x = 2\)) is \(\vert6 - 2\vert=4\).

Step3: Use the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). Substituting \(base = 8\) and \(height=4\), we have \(A=\frac{1}{2}\times8\times4\).

$$A=\frac{1}{2}\times32 = 16$$

Answer:

A. 16 square units