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Then/Now I CAN find the distance between two points and the midpoint of a segment. Learning Target

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Concept Distance - the length of the segment between two endpoints.

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Example 1 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 3Simplify. Answer: 3

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A.A B.B C.C D.D Example 1 A.2 B.8 C.–2 D.–8 Use the number line to find AX. Do Page 30 # 1-2

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Concept

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Example 2 Find Distance on a Coordinate Plane Find the distance between E(–4, 1) and F(3, –1). (x 1, y 1 ) = (–4, 1) and (x 2, y 2 ) = (3, –1)

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Example 2 Find Distance on a Coordinate Plane CheckGraph the ordered pairs and check by using the Pythagorean Theorem.

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Example 2 Find Distance on a Coordinate Plane.

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A.4 B. C. D. A.A B.B C.C D.D Example 2 Find the distance between A(–3, 4) and M(1, 2). Do Page 30 # 3-6

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Concept Midpoint - the point half way between the endpoints of a segment.

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Example 3 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 x 1 = 2.5, x 2 = 10

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Example 3 Find Midpoint on a Number Line Simplify. Answer: The midpoint of the couch back is 6.25 feet from the wall.

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A.A B.B C.C D.D Example 3 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

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Concept

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Example 4 Find Midpoint in Coordinate Plane Answer: (–3, 3)

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A.A B.B C.C D.D Example 4 A.(–10, –6) B.(–5, –3) C.(6, 12) D.(–6, –12) Do Page 30 # 9-10

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Example 5 Find the Coordinates of an Endpoint Write two equations to find the coordinates of D. Let D be (x 1, y 1 ) and F be (x 2, y 2 ) in the Midpoint Formula. (x 2, y 2 ) =

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Example 5 Find the Coordinates of an Endpoint Answer: The coordinates of D are (–7, 11). Midpoint Formula

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A.A B.B C.C D.D Example 5 A.(3.5, 1) B.(–10, 13) C.(15, –1) D.(17, –11) Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5). Do Page 31 # 11

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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.

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Example 6 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.

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Example 6 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.

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Original measure Example 6 Use Algebra to Find Measures

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Example 6 Use Algebra to Find Measures Check QR = 6 – 3x Original Measure

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Example 6 Use Algebra to Find Measures Multiply. Simplify.

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A.A B.B C.C D.D Example 6 A.1 B.3 C.5 D.10 Do Page 31 #12

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