Distance Formula

Lesson

Distance formula

[Formula]

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).

Solution

Recall the distance formula

Let x₁ = 8,   x₂ = 4,   y₁ = 6,   y₂ = 2

Repeating the process:

Let x₁ = 9,   x₂ = 13,   y₁ = 4,   y₂ = 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

Explanation

The distance between 2 points (x₁, y₁) and (x_2, y₂) is found using the formula

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

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