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) | Distance Formula

= | –3 | or 3 Simplify.

Answer: 3

Use the number line to find AX.

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

2 21 2 1 2( ) ( )d x x y y

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)

Find Distance on a Coordinate Plane

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

Draw a sketch of this graph on your paper.

Find Distance on a Coordinate Plane

.

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

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)

Find the Coordinates of an Endpoint

Write two equations to find the coordinates of D.

Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.

(x2, y2) = (–5, –3)

Find the Coordinates of an Endpoint

Answer: The coordinates of D are (–7, 11).

Midpoint Formula

Midpoint Formula

5 minutes

Skills Packet

Do 9 and 10

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

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

Use Algebra to Find Measures

• Constructions p. 30 ‘Bisect a Segment

• HW Skills Packet 1-7, 12-16 all