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 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

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

Can distance ever be negative?

Example 1 A.2 B.8 C.–2 D.–8 Use the number line to find AX.

Concept You will need a scientific calculator to do this problem 1.Put x’s and y’s in the formula 2.Subtract x’s and square 3.Subtract y’s and square 4.Add numbers under the radical 5.Take square root if answer is in decimal form.

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 1.Add the x’s and divide by 2 2.Add the y’s and divide by 2

Assignment Day 1 p. 31, odd No work, No credit!

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? 1 mile = 5280 feet

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

Segment Bisector A segment bisector is any segment, line, or line that intersects a segment at its midpoint.

Construction: Bisect a Segment 1.Draw a segment. 2.Place the compass on one end and open the compass bigger than half of the segment. 3.Draw arcs above and below the segment. 4.Without moving the compass sixe, move the point to the other end of the segment. 5.Draw arcs about and below the segment. 6.Use a straightedge to connect the x’s you made above and below the segment. 7.Where this new segment crosses the 1 st one is the midpoint. See page 30 for pictures.

Assignment 1-3 p. 31, even, odd No work, No credit