4.1/4.6 Midpoint & SlopeI can apply the midpoint formula.

Day 3

I can understand the concept of slope.

1. On the same coordinate plane, draw the following:

a) the line through (3, 5) & (8, 7)

b) the line through (3, 12) that is parallel to the line through (3, 5) & (8, 7)

Find the coordinates of at least one more point on the line you drew for (b)

c) the line through (3, 12) that is perpendicular to the line that you drew in (b)

Find the coordinates of at least one more point on the line you drew for (c)

I can recognize the relationships of parallel & perpendicular slopes.

Midpoint

Definition: The midpoint of a line segment is the point directly in the middle of the segment.

If you are give two coordinates and use the following formula to find the midpoint:

1 1,x y 2 2,x y

1 2 1 2,2 2

x x y yM

** Remember median uses midpoint too

Find the coordinates of the midpoint of each side of △WAY

Example 1

W (2,4)

Y (6,-2)A (-2,-2)

Given: is a diameter of ʘO Find: the coordinates of O

Example 2

W(1,3)

C(-3,-1)

O

Slope

Definition: The slope of a line is a comparison between the amount a line rises to the amount it moves left or right.

2 1

2 1

y yrisem

run x x

where m is the slope of the line

If you are given two coordinates and use the following formula to find the slope

1 1,x y 2 2,x y

m = 0◦ Horizontal line

m = = undefined◦ Vertical line

Special cases

Find the slope of the line containing (7,5) and (-3,2).

Example 3

Are (12,18), (15,25), and (21,39) collinear?(Hint: to be collinear all three pairs of points must have the same slope)

Example 4

Parallel lines are lines that have the same slopes. (//)

Parallel and perpendicular lines

Perpendicular lines have opposite reciprocal slopes. (⊥)

** Remember altitudes

Is ∠A a right angle? Justify your answer.

Example 5

D(1,5) Y(7,5)

A(4,1)

What is the slope of the line parallel to the line containing (5,-3) and (9,-1)?

Example 6

What is the slope of a line perpendicular to a line with slope 2?

Example 7