Question

find the distance between f and g.
the distance between f and g is
(type an exact answer using radicals as needed.)
f(4,8)
g(14,12)

Explanation:

Step1: Identify coordinates of F and G

F is at \((4, 8)\), G is at \((14, 12)\).

Step2: Apply distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Let \(x_1 = 4\), \(y_1 = 8\), \(x_2 = 14\), \(y_2 = 12\).
Substitute into formula: \(d = \sqrt{(14 - 4)^2 + (12 - 8)^2}\)

Step3: Simplify inside the square root

\(14 - 4 = 10\), \(12 - 8 = 4\). So \(d = \sqrt{10^2 + 4^2} = \sqrt{100 + 16}\)

Step4: Add the terms inside

\(100 + 16 = 116\), so \(d = \sqrt{116}\)

Step5: Simplify the radical

\(\sqrt{116} = \sqrt{4 \times 29} = 2\sqrt{29}\)

Answer:

\(2\sqrt{29}\)