Do Now: Label the plane below

Objectives

SWBAT use the midpoint and distance formulas.

Definitions

Midpoint: If a point is a midpoint, then it divides the segment into two congruent segments. If a point divides a segment into two congruent segments, then it is a midpoint.

•Segment Bisector:• If a segment is bisected, then it is divided at the midpoint. If a segment is divided at the midpoint, then it is bisected

Congruence:If two objects are congruent, then they are exactly the same size and shape. If two objects are exactly the same size and shape, then they are congruent. Congruence is marked with lines (show example of congruent lines in diagram) and we write the congruence symbol between the segments.

Example 1: If you know that B is the midpoint of AC and AB is 4, then what is BC? How did you solve?

Statement Reason1. B is the midpoint of AC 1. Given2. AB = 4 2. Given3. AB = BC 3. If B is the midpoint of AC,

then it divides AC into two congruent segments.

4. BC = 4 4. If AB = BC, then BC = 4 by substitution.

Example 2: If AC is 6, and B is the midpoint, what’s BC? How did you figure that out? Now let’s prove it.

Statement Reason

Example 3: If AF = 2x + 3 and FC = 4x – 1, and AC is bisected by BF, solve for xStatement Reason

Formulas

Midpoint Formula

Distance Formula

Steps for finding the midpoint

1) Write the formula2) Substitute3) Add4) Divide

Example 1

Example 2

On a coordinate grid, a bakery is located at (2, 6). A barber shop is located at (-4, 4). Which point is exactly between the bakery and the barber shop?

Steps for finding the distance (look on page 18)1. Substitute2. Subtract3. Square4. Add5. Find the square root

Example 3

Example 4

Guided Practice: Let’s Solve a Mystery!

Independent Practice

See the handout!