Question

what is the area of the triangle? square units

Explanation:

Step1: Find the base length

The two points \((2,7)\) and \((2, - 2)\) have the same \(x\) - coordinate. The distance between them (base of the triangle) is calculated using the distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1 = x_2\), \(d=\vert y_1 - y_2\vert\).
So, \(b=\vert7-(-2)\vert=\vert7 + 2\vert=9\)

Step2: Find the height

The height is the horizontal distance from the line \(x = 2\) (where the base is located) to the point \((6,4)\). Since the \(x\) - coordinate of the base - line is \(x = 2\) and the \(x\) - coordinate of the other point is \(x = 6\), \(h=\vert6 - 2\vert=4\)

Step3: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\).
Substitute \(b = 9\) and \(h = 4\) into the formula: \(A=\frac{1}{2}\times9\times4\)
\(A=\frac{1}{2}\times36 = 18\)

Answer:

\(18\)