Students will be able to find midpoint of a segment Objective: Students will be able to find midpoint of a segment Students will be able to find the distance between 2 points. Splash Screen

Mathematical Practices 2 Reason abstractly and quantitatively. 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. CCSS

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

distance irrational number midpoint segment bisector Vocabulary

Concept

Use the number line to find QR. 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 3 Simplify. Answer: 3 Example 1

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

Concept

Find the distance between E(–4, 1) and F(3, –1). Find Distance on a Coordinate Plane Find the distance between E(–4, 1) and F(3, –1). (x1, y1) = (–4, 1) and (x2, y2) = (3, –1) Example 2

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

Find Distance on a Coordinate Plane . Example 2

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

Concept

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 x1 = 2.5, x2 = 10 Example 3

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

DRAG RACING The length of a drag racing strip is. mile long 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? A. 330 ft B. 660 ft C. 990 ft D. 1320 ft Example 3

Concept

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

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

Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula. Find the Coordinates of an Endpoint Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula. (x2, y2) = (–5, –3) Write two equations to find the coordinates of D. Example 5

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

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

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

Plan Because Q is the midpoint, you know that Use Algebra to Find Measures Plan Because Q is the midpoint, you know that Use this equation and the algebraic measures to find a value for x. Solve Subtract 1 from each side. Example 6

Use Algebra to Find Measures Original measure Example 6

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

Use Algebra to Find Measures Multiply. Simplify. Example 6

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

Homework Page 31 (14-30 even, 34-46 even, 47-48, 53-54