Question

3. (-4,5) and (-8,-5) __

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Answer

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BethanElite · Tutor for 8 years

Answer

\(\sqrt{116}\)

Explain

The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:\[d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\]Substituting the given points into the formula, we get:\[d = \sqrt{((-8) - (-4))^2 + ((-5) - 5)^2}\]Simplify the expression inside the square root:\[d = \sqrt{(-8 + 4)^2 + (-5 - 5)^2}\]\[d = \sqrt{(-4)^2 + (-10)^2}\]\[d = \sqrt{16 + 100}\]\[d = \sqrt{116}\]Therefore, the distance between the points (-4,5) and (-8,-5) is \(\sqrt{116}\).

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