In this lesson, students continue to apply the Pythagorean Theorem by finding distances between points in the coordinate plane.

Students begin by finding and ordering distances between pairs of points that lie on the same vertical or horizontal line. Next, they find the distances between three points in the coordinate plane that, if connected, would make a right triangle. Students see that to find the distance between two points (or the length of the segment connecting those two points), they can draw a right triangle and use the Pythagorean Theorem (MP7).

Next, groups of students find the distance between two points, given only their coordinates. Whether students plot these points first or go straight to using an algebraic set of steps, they must think about how to generalize and communicate their method (MP6). 

This lesson contains an optional activity where students find the perimeter of triangles drawn on a coordinate plane without a grid. This activity can be useful if students need additional practice finding the length of a segment that does not lie along a gridline.