Question

a triangle has vertices on a coordinate grid at ( e(-1,-8), f(4,-8) ), and ( g(4,10) ). what is the length, in units, of ( overline{ef} )?

Explanation:

Step1: Identify the coordinates

The coordinates of \(E\) are \((-1,-8)\) and of \(F\) are \((4,-8)\). The \(y\)-coordinates are the same (\(y=-8\) for both points).

Step2: Use the distance formula for horizontal line

When \(y_1 = y_2\), the distance \(d=\vert x_2 - x_1\vert\). Here \(x_1=-1\), \(x_2 = 4\). So \(d=\vert4-(-1)\vert=\vert4 + 1\vert\).

Step3: Calculate the absolute value

\(\vert4 + 1\vert=\vert5\vert=5\).

Answer:

\(5\)