Question

how would you set up the distance formula to find the distance between points e and f?
(1 point)
\\( \circ d = \sqrt{(2 - 6)^2 + (5 - 1)^2} \\)
\\( \circ d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \\)
\\( \circ d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \\)
\\( \circ d = \sqrt{((-2) + 6)^2 + (5 + 1)^2} \\)

Explanation:

Step1: Recall Distance Formula

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

Step2: Identify Coordinates of E and F

From the grid (assuming E is \((2,5)\) and F is \((6,1)\) as per the options, since we need to check which option uses correct \((x_2 - x_1)\) and \((y_2 - y_1)\)). For points \(E(x_1,y_1)=(2,5)\) and \(F(x_2,y_2)=(6,1)\), substituting into the formula: \(x_2 - x_1=6 - 2\), \(y_2 - y_1=1 - 5\). So the distance formula setup is \(d=\sqrt{(6 - 2)^2+(1 - 5)^2}\).

Answer:

\(d = \sqrt{(6 - 2)^2+(1 - 5)^2}\) (the third option: \(d=\sqrt{(6 - 2)^{2}+(1 - 5)^{2}}\))