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Lesson Menu Five-Minute Check (over Lesson 1–2) CCSS Then/Now New Vocabulary Key Concept: Distance Formula (on Number Line) Example 1:Find Distance on a Number Line Key Concept: Distance Formula (in Coordinate Plane) Example 2:Find Distance on Coordinate Plane Key Concept: Midpoint Formula (on Number Line) Example 3:Real-World Example: Find Midpoint on Number Line Key Concept: Midpoint Formula (in Coordinate Plane) Example 4:Find Midpoint in Coordinate Plane Example 5:Find the Coordinates of an Endpoint Example 6:Use Algebra to Find Measures

Over Lesson 1–2 5-Minute Check 1 What is the value of x and AB if B is between A and C, AB = 3x + 2, BC = 7, and AC = 8x – 1? A.x = 2, AB = 8 B.x = 1, AB = 5 C. D.x = –2, AB = –4

Over Lesson 1–2 5-Minute Check 2 A.x = 1, MN = 0 B.x = 2, MN = 1 C.x = 3, MN = 2 D.x = 4, MN = 3 If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, what is the value of x and MN?

Over Lesson 1–2 5-Minute Check 3 Find RT. A. B. C. D... in.

Over Lesson 1–2 5-Minute Check 4 What segment is congruent to MN? A.MQ B.QN C.NQ D.no congruent segments

Over Lesson 1–2 5-Minute Check 5 What segment is congruent to NQ? A.MN B.NM C.QM D.no congruent segments

Over Lesson 1–2 5-Minute Check 6 A.5 B.6 C.14 D.18

CCSS Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 7 Look for and make use of structure.

Then/Now You graphed points on the coordinate plane. Find the distance between two points. Find the midpoint of a segment.

Vocabulary distance irrational number midpoint segment bisector

Concept

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

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.

Example 2 Find Distance on a Coordinate Plane.

A.4 B. C. D. Example 2 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 Find Midpoint on a Number Line Simplify. Answer: The midpoint of the couch back is 6.25 feet from the wall.

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)

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. (x 2, y 2 ) = (–5, –3)

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

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. Solve Subtract 1 from each side. Plan Because Q is the midpoint, you know that

Original measure Example 6 Use Algebra to Find Measures

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

Example 6 Use Algebra to Find Measures Multiply. Simplify.

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

End of the Lesson