GEOMETRY WITH MR. REEVES 1.3 Using Midpoint and Distance Formulas

1.3 Using Midpoint and Distance Formulas

• Find segment lengths using midpoints and segment bisectors

• Use the Midpoint Formula

• Use the Distance Formula

VOCABULARY

WHAT YOU WILL LEARN

• midpoint • segment bisector

Vocabulary: Midpoint

• The midpoint of a segment is the point that divides the segment into two congruent segments.

Vocabulary: Segment Bisector

• A segment bisector is a point, ray, line, line segment, or plane that intersects the segment at its midpoint. A midpoint or segment bisector bisects a segment.

Example 1

Your turn…

• Complete Monitoring Progress #1-2 in your notebooks:

Example 2

Your turn…

• Complete Monitoring Progress #3-4 in your notebooks:

Construction

• Construct a segment bisector by paper folding. Then, find the midpoint.

Exploration: Midpoint Formula

Midpoint Formula

• The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints.

Example 3

Your turn…

• Complete Monitoring Progress #5-8 in your notebooks:

Exploration: Distance Formula

The Distance Formula is related to the Pythagorean Theorem, which you will see again when you work with right triangles.

Distance Formula

• You can use the Distance Formula to find the distance between two points in a coordinate plane.

Example 4

• Your school is 4 miles east and 1 mile south of your apartment. A recycling center, where your class is going on a field trip, is 2 miles east and 3 miles north of your apartment. Estimate the distance between the recycling center and your school.

Your turn…

• Complete Monitoring Progress #9 in your notebooks:

Monitoring Progress Answers

1.3 Using Midpoint and Distance Formulas

• Find segment lengths using midpoints and segment bisectors

• Use the Midpoint Formula

• Use the Distance Formula

VOCABULARY

WHAT YOU LEARNED

• midpoint • segment bisector