Go the Distance

Learning Focus

Use the distance formula on the coordinate plane.

Big idea

Distance between $(x_1,y_1)$ and $(x_2,y_2)$:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

It is the Pythagorean theorem on a coordinate grid.

Worked example

Distance from $(1,2)$ to $(4,6)$:

$\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$.

Takeaways

• Distance is always nonnegative.
• Horizontal/vertical segments simplify to a single difference.