Chapter 1.3 Distance and Measurement. Distance (between two points)- the length of the segment with those points as its endpoints. Definition.

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Sec 1-3 Concept: Use Midpoint and Distance Formulas

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Presentation transcript:

Chapter 1.3 Distance and Measurement

Distance (between two points)- the length of the segment with those points as its endpoints. Definition

Concept

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

A.2 B.8 C.–2 D.–8 Use the number line to find AX.

Concept

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)

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

Find Distance on a Coordinate Plane.

Find the distance between A(-3, 8) and B(-5, 2)

A.4 B. C. D. Find the distance between A(–3, 4) and M(1, 2).

Concept

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

Example 3 A.330 ft B.660 ft C.990 ft D.1320 ft The length of a drag racing strip is a quarter of a mile long. How many feet from the finish line is the midpoint of the racing strip?

Concept

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

A.(–10, –6) B.(–5, –3) C.(6, 12) D.(–6, –12)

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 ) = (–5, –3)

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

Find the coordinates of the missing endpoint if Y is the midpoint of XZ: X(-4, 2) and Y(6, -1)

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).

Segment Bisector Any segment, line, or plane that intersects a segment at its midpoint is called a segment bisector. In the figure, M is the midpoint of line AB. Line XY is the segment bisector of line AB. X Y M

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.

Suppose S is the midpoint of RT. RS = 3x – 4, ST = 5x – 26, Find the measure of RT.

A.1 B.10 C.5 D.3

Pg. 30 #1-12 Try it!