Objective Students will be able to find midpoint

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

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.

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

• distance • irrational number • midpoint • segment bisector

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) | = | – 3 | or 3 Answer: 3 Distance Formula Simplify.

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

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 Check Graph the ordered pairs and check by using the Pythagorean Theorem.

Find Distance on a Coordinate Plane .

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

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

Find Midpoint on a Number Line Simplify. Answer: The midpoint of the couch back is 6. 25 feet from the wall.

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

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

Find the Coordinates of an Endpoint Let D be (x 1, y 1) and F be (x 2, y 2) in the Midpoint Formula. (x 2, y 2) = (– 5, – 3) Write two equations to find the coordinates of D.

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

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

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.

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.