Question

Calculate the distance between the points H=(3,-1) and E=(8,-5) in the coordinate plane. Give an exact answer (not a decimal approximation).​

Answer 1

Answer: $\sqrt{41}$

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Work Shown:

Use the distance formula.

$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-1-(-5))^2+(3-8)^2}\\\\d = \sqrt{(-1+5)^2+(3-8)^2}\\\\d = \sqrt{(4)^2+(-5)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41}$

Or you could use the pythagorean theorem, which is how the distance formula is set up.