Distance Math Example 2

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Example 2

medium
Find the distance between P(−2,3)P(-2, 3) and Q(4,−1)Q(4, -1). Leave your answer in simplest radical form.

Solution

  1. 1
    Step 1: d=(4−(−2))2+(−1−3)2d = \sqrt{(4-(-2))^2 + (-1-3)^2}.
  2. 2
    Step 2: d=62+(−4)2=36+16=52d = \sqrt{6^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52}.
  3. 3
    Step 3: Simplify: 52=4×13=213\sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}.

Answer

d=213d = 2\sqrt{13} units
Simplifying surds: factor out perfect squares from under the radical. 52=4×1352 = 4 \times 13, so 52=213\sqrt{52} = 2\sqrt{13}. Always check for common square factors (4, 9, 16, 25, ...) when simplifying.

About Distance

The length of the shortest path between two points, always a non-negative real number.

Learn more about Distance →

More Distance Examples

Example 1 easy

Find the distance between points [formula] and [formula].

Example 3 easy

What is the distance from the origin [formula] to the point [formula]?

Example 4 hard

Find the distance between points [formula] and [formula] in 3D space.

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