- Use the Pythagorean Theorem to find the distance between two points
The Pythagorean Theorem connects directly to the distance formula on the coordinate plane. To find the distance between two points, think of the segment between them as the hypotenuse of a right triangle.
distance formula
For points [latex](x_1, y_1)[/latex] and [latex](x_2, y_2)[/latex]:
[latex]\begin{align} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \end{align}[/latex]
This formula comes from [latex]a^2 + b^2 = c^2[/latex].
Find the distance between [latex](1, 2)[/latex] and [latex](5, 8)[/latex].
[latex]\begin{align} d &= \sqrt{(5 - 1)^2 + (8 - 2)^2} \\ &= \sqrt{4^2 + 6^2} \\ &= \sqrt{16 + 36} \\ &= \sqrt{52} \\ &\approx 7.21 \end{align}[/latex]
The distance between the points is approximately 7.21 units.