4.1 Distance and 4.1 Distance and Midpoint FormulasMidpoint Formulas4.1 Distance and 4.1 Distance and

Midpoint FormulasMidpoint Formulas

Standards: MM1G1a and Standards: MM1G1a and MM1G1cMM1G1c

Midpoint Formula

Midpoint Formula

(Ex 1) Find a midpoint of a line segment.

Find the midpoint of the line segment with endpoints (-3, 7) and (-1, 11).

(Ex 2) Find a missing coordinate

Find the missing coordinate given that the midpoint (1, 3) is between the 2 points (-1, 8) and (x, y).

Checkpoint1. Find the midpoint: (1, -2) and (5, -4)

2. Find the midpoint: (5, 12) and (13, 8)

3. Find the missing coordinate.Midpoint (-1, 3). Endpoints: (2, 4) and (x, y)

Distance Formula

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

Distance Formula

(Ex 3) Find the distance between 2 points

Find the distance between (4, -3) and (-7, 2).

(Ex 4) Find a missing coordinate.

The distance between (5, a) and (9,6) is 4 2 units. Find the possible values of a.

Checkpoint4. Find the distance between (2, -3)

and (5, 1).

5. The distance between (-1, 2) and (3, b) is 41 units. Find the possible values of b.

(Ex 5) Find the midpoint and length of the line segments.

(Ex 6) “Real”-world example

On a road trip, you hike 3 miles north and 2miles west. Starting at the same point, your friend hikes 4 miles east and 1 mile south.

How far apart are you?

If you want to meet for lunch, where could you meet so each person goes the same distance?

(Ex 7) Find the distance between a point and a

line.What is the distance from point B to

line q?B

q

(1, 4)

(4, 1)

(1, -2)

Checkpoint6. Find the distance from point A to

line c.

Assignment

p. 195 #2-8 (even), 16-22 (even)

p. 232 #20 and 22