Question

how would you set up the distance formula to find the distance between points e and f.

Explanation:

Step1: Identify coordinates of E and F

From the graph, let's assume point E is at \((-5, 0)\) (since the line starts at x = -5, y = 0) and point F is at \((2, -5)\).

Step2: Recall distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step3: Substitute coordinates into formula

Substitute \(x_1 = -5\), \(y_1 = 0\), \(x_2 = 2\), \(y_2 = -5\) into the formula. So the distance formula setup is \(d = \sqrt{(2 - (-5))^2 + (-5 - 0)^2}\) which simplifies to \(d = \sqrt{(2 + 5)^2 + (-5 - 0)^2}=\sqrt{7^2 + (-5)^2}\).

Answer:

To find the distance between points \( E(-5, 0) \) and \( F(2, -5) \), we use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Substituting \( x_1=-5, y_1 = 0, x_2=2, y_2=-5 \), we get \( d=\sqrt{(2 - (-5))^2+(-5 - 0)^2}=\sqrt{7^2+(-5)^2} \).