1. Distance on the Coordinate Plane
Lesson 19
Lines & Angles
Distance on the Coordinate Plane

2. Warm-Up
1. Draw a coordinate plane with the x- and y-axes from −10 to 10.
2. Graph the following points on the coordinate plane.
A(3, 4)
B(−2, 6)
C(9, −5)
D(0, −3)
E(−8, 0)

3. Distance on the Coordinate Plane
Target:
Find the distance between two points on the coordinate
plane using the Pythagorean Theorem.

5. Finding Distance on a Coordinate Plane
Graph the two ordered pairs. Connect the points and label the segment c.
Using c as the hypotenuse of a right triangle, draw the legs of the triangle.
Find the lengths of the legs.
Use the Pythagorean Theorem to find the length of the hypotenuse c. This length is the distance between the two points on the coordinate plane.

6. Example 1
Find the distance between (1, 3) and (4, –2). Round to the nearest tenth. First, graph the points. Connect with line segment c. Draw a right triangle with c as the hypotenuse. The legs are 3 and 5. Use the Pythagorean Theorem: 3 5
The distance between (1, 3) and (4, –2) is about 5.8 units.

7. Exit Problems Find the distance between each set of points. Round to
the nearest tenth, when necessary.
(1, 4) and (9, 10)
(−3, 2) and (1, −6)

8. Communication Prompt What process you would use to find the
distance between (2, 7) and (4, 10)?