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What is the distance between the points (-1, 5) and (-7, -3)?


Question

What is the distance between the points (-1, 5) and (-7, -3)?

Options

A) 9

B) 10

C) 11

D) 12

The correct answer is B.

Explanation:

The distance \((d)\) between two points \((x_1y_1)\) is given as:
\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
For the points \((-1,5)\) and \((-7,-3)\)
\(x_1 = -1, y_1 = 5, x_2 = -7\) and \(y_2 = -3\)
\(d = \sqrt{[-7-(-1)]^2 + [-3-5]^2}\)
\(= \sqrt{(-7+1)^2+(-8)^2}\)
\(= \sqrt{(-6)^2 + (-8)^2}\)
\(= \sqrt{36 + 64} = \sqrt{100} = 10\)
\(d = 10\) units

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Dicussion (1)

  • The distance \((d)\) between two points \((x_1y_1)\) is given as:
    \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
    For the points \((-1,5)\) and \((-7,-3)\)
    \(x_1 = -1, y_1 = 5, x_2 = -7\) and \(y_2 = -3\)
    \(d = \sqrt{[-7-(-1)]^2 + [-3-5]^2}\)
    \(= \sqrt{(-7+1)^2+(-8)^2}\)
    \(= \sqrt{(-6)^2 + (-8)^2}\)
    \(= \sqrt{36 + 64} = \sqrt{100} = 10\)
    \(d = 10\) units

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