QuestionAugust 25, 2025

Find the distance between the points (2,6) and (8,8) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units

Find the distance between the points (2,6) and (8,8) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units
Find the distance between the points (2,6) and (8,8) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units

Solution
4.4(263 votes)

Answer

2\sqrt{10} units Explanation 1. Identify the coordinates The points are (x_1, y_1) = (2, 6) and (x_2, y_2) = (8, 8). 2. Apply the distance formula Use **d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}**. 3. Substitute the values d = \sqrt{(8 - 2)^2 + (8 - 6)^2} = \sqrt{6^2 + 2^2}. 4. Simplify the expression d = \sqrt{36 + 4} = \sqrt{40}. 5. Simplify the radical d = \sqrt{4 \times 10} = 2\sqrt{10}.

Explanation

1. Identify the coordinates<br /> The points are $(x_1, y_1) = (2, 6)$ and $(x_2, y_2) = (8, 8)$.<br />2. Apply the distance formula<br /> Use **$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$**.<br />3. Substitute the values<br /> $d = \sqrt{(8 - 2)^2 + (8 - 6)^2} = \sqrt{6^2 + 2^2}$.<br />4. Simplify the expression<br /> $d = \sqrt{36 + 4} = \sqrt{40}$.<br />5. Simplify the radical<br /> $d = \sqrt{4 \times 10} = 2\sqrt{10}$.
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