Question

find the distance between the pair of points.
e(3, -1), f(-3,7)

d = \boxed{} (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(E(3,-1)\) and \(F(-3,7)\), \(x_1 = 3\), \(y_1=-1\), \(x_2=-3\), \(y_2 = 7\).

Step2: Substitute values into formula

Substitute into the formula: \(d=\sqrt{(-3 - 3)^2+(7 - (-1))^2}\)

Step3: Simplify inside the square root

Simplify each term: \((-3 - 3)=-6\), so \((-6)^2 = 36\); \(7-(-1)=8\), so \(8^2=64\). Then \(d=\sqrt{36 + 64}\)

Step4: Add inside the square root

\(36+64 = 100\), so \(d=\sqrt{100}\)

Step5: Simplify the square root

\(\sqrt{100}=10\)

Answer:

\(10\)