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Lesson

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Distance formula

[Formula]

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Example

Show that the distance between the two points (8,6) and (4,2) is the same as the distance between the two points (9,4) and (13, 0).

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Solution

Recall the distance formula

Let x₁ = 8,Ìý Ìýx₂ = 4,Ìý Ìýy₁ = 6,Ìý Ìýy₂ = 2

Repeating the process:

Let x₁ = 9,Ìý Ìýx₂ = 13,Ìý Ìýy₁ = 4,Ìý Ìýy₂ = 0

Therefore:

d₁ = d₂

and so the distance between the two sets of points are equal

Question

Determine the distance between the points (-5,-7) and (-3,1), simplifying your answer where necessary

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Explanation

The distance between 2 points (x₁, y₁) and (x_2,Ìýy₂) is found using the formula

When applied to the points (-5,-7) and (-3,1), we have

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