QuestionAugust 25, 2025

Find the distance between the points (-4,-7) and (2,0) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units

Find the distance between the points (-4,-7) and (2,0) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units
Find the distance between the points (-4,-7) and (2,0) Write your answer as a whole number or a fully simplified radical expression. Do not round. square units

Solution
4.5(244 votes)

Answer

\sqrt{85} units Explanation 1. Identify the coordinates The points are (-4, -7) and (2, 0). 2. Apply the distance formula Use **d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}** where (x_1, y_1) = (-4, -7) and (x_2, y_2) = (2, 0). 3. Substitute the values d = \sqrt{(2 - (-4))^2 + (0 - (-7))^2} = \sqrt{(2 + 4)^2 + (0 + 7)^2}. 4. Simplify inside the square root d = \sqrt{6^2 + 7^2} = \sqrt{36 + 49}. 5. Calculate the final expression d = \sqrt{85}.

Explanation

1. Identify the coordinates<br /> The points are $(-4, -7)$ and $(2, 0)$.<br /><br />2. Apply the distance formula<br /> Use **$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$** where $(x_1, y_1) = (-4, -7)$ and $(x_2, y_2) = (2, 0)$.<br /><br />3. Substitute the values<br /> $d = \sqrt{(2 - (-4))^2 + (0 - (-7))^2} = \sqrt{(2 + 4)^2 + (0 + 7)^2}$.<br /><br />4. Simplify inside the square root<br /> $d = \sqrt{6^2 + 7^2} = \sqrt{36 + 49}$.<br /><br />5. Calculate the final expression<br /> $d = \sqrt{85}$.
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