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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