Question

find the distance between the two points in simplest radical form.
(8, -4) and (3, 8)

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Let \((x_1, y_1) = (8, -4)\) and \((x_2, y_2) = (3, 8)\).

Step3: Substitute into formula

Calculate \( x_2 - x_1 = 3 - 8 = -5 \) and \( y_2 - y_1 = 8 - (-4) = 12 \).
Then \( d = \sqrt{(-5)^2 + 12^2} \).

Step4: Simplify the expression

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Answer:

Step1: Recall distance formula

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

Step2: Identify coordinates

Let \((x_1, y_1) = (8, -4)\) and \((x_2, y_2) = (3, 8)\).

Step3: Substitute into formula

Calculate \( x_2 - x_1 = 3 - 8 = -5 \) and \( y_2 - y_1 = 8 - (-4) = 12 \).
Then \( d = \sqrt{(-5)^2 + 12^2} \).

Step4: Simplify the expression

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