Splash Screen. Then/Now You graphed points on the coordinate plane. (Lesson 0–2) Find the distance between two points. Find the midpoint of a segment.

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Presentation transcript:

Splash Screen

Then/Now You graphed points on the coordinate plane. (Lesson 0–2) Find the distance between two points. Find the midpoint of a segment.

Vocabulary distance midpoint segment bisector

Concept Or how far is it from one point to the other.

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 Or how far is it from Q to R? 12 3

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.

Concept

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)

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

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).

Concept Or find the average of the two endpoints.

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?

Concept

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

A.A B.B C.C D.D Example 4 A.(–10, –6) B.(–5, –3) C.(6, 12) D.(–6, –12)

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.

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

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).

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.

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.

Original measure Example 6 Use Algebra to Find Measures

A.A B.B C.C D.D Example 6 A.1 B.3 C.5 D.10