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 Use the number line to find AX.

Concept Switching both coordinates in the formula will give the same result for the distance. See below.

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. Draw a sketch of this graph on your paper.

Example 2 Find Distance on a Coordinate Plane.

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

Chapter 1 Overview Video Distance and Midpoint Skills Packet Do 7 and 8 (find the distance only) Now let’s do the Reach test questions 1-3

Concept

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

Class Assignment - 8 minutes Distance and Midpoint Skills Packet Do 4, 5 and 8 (Find the midpoint only)

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

5 minutes Skills Packet Do 9 and 10

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

Constructions p. 30 ‘Bisect a Segment

HW Skills Packet 1-7, all