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• I CAN find the distance between two points and the midpoint of a segment.
Learning Target
• Distance - the length of the segment between two endpoints.
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.
Answer: 3
A. A
B. B
C. C
D. D
A. 2
B. 8
C. –2
D. –8
Use the number line to find AX.
Do Page 30 # 1-2
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and (x2, y2) = (3, –1)
Find Distance on a Coordinate Plane
Check Graph the ordered pairs and check by using the Pythagorean Theorem.
A. 4
B.
C.
D.
A. A
B. B
C. C
D. D
Find the distance between A(–3, 4) and M(1, 2).
Do Page 30 # 3-6
• Midpoint - the point half way between the endpoints of a segment.
Find Midpoint on a Number Line
DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet?
First we must convert 90 inches to 7.5 feet. The coordinates of the endpoints of the couch are 2.5 and 10. Let M be the midpoint of the couch.
Midpoint Formula
x1 = 2.5, x2 = 10
Find Midpoint on a Number Line
Simplify.
Answer: The midpoint of the couch back is 6.25 feet from the wall.
A. A
B. B
C. C
D. D
A. 330 ft
B. 660 ft
C. 990 ft
D. 1320 ft
DRAG RACING The length of a drag racing strip is
mile long. How many feet from the finish line is
the midpoint of the racing strip?
Do Page 30 # 7-8
A. A
B. B
C. C
D. D
A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Do Page 30 # 9-10
Find the Coordinates of an Endpoint
Write two equations to find the coordinates of D.
Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
(x2, y2) =
Find the Coordinates of an Endpoint
Answer: The coordinates of D are (–7, 11).
Midpoint Formula
Midpoint Formula
A. A
B. B
C. C
D. D
A. (3.5, 1)
B. (–10, 13)
C. (15, –1)
D. (17, –11)
Find the coordinates of R if N (8, –3) is the midpointof RS and S has coordinates (–1, 5).
Do Page 31 # 11
• Segment Bisector – a segment, line, or plane that intersects a segment at its midpoint.
• In the diagram, M is the midpoint of segment PQ, so segment JM, line KM, and plane A are all segment bisectors of segment PQ.
Use Algebra to Find Measures
Understand You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR.
Use Algebra to Find Measures
Use this equation and the algebraic measures to find a value for x.
Plan Because Q is the midpoint, you know
that
Solve
Subtract 1 from each side.
Use Algebra to Find Measures
Check
QR = 6 – 3x Original Measure
A. A
B. B
C. C
D. D
A. 1
B. 3
C. 5
D. 10Do Page 31 #12
