Distance and Midpoint

1.1 Distance and Midpoint

Distance Formula – know by heart!

for and

Midpoint formula for a segment with endpoints A and B – know by heart

for and

additional practice :

simplify

simplify -2⁰

Examples

Given the following points, find the distance between them and the midpoint of the
segment joining them. Sketch a little graph of the segment being sure to use appropriate
scaling.

A. ( 1, 2) and ( 5, -3)

Distance

Midpoint

big hint 9(16) = 144

Distance

Midpoint

big hint 9(16) + 25 = 169

Distance

Midpoint

1.2 Lines

Review
Ax + By + C = 0
is the General Equation of a Line

Parts of a line:
x intercept – where the line hits the x axis, y = 0
y intercept – where the line hits the y axis, x = 0
slope – a number that measures incline

Example A:
8x - 2y - 10 = 0

The first row shows the coordinates of the y intercept .
The second row shows the coordinates of the x intercept.

From this we can calculate the slope

Example B:
6x - 3y - 18 = 0

The first row shows the coordinates of the y intercept.
The second row shows the coordinates of the x intercept.

From this we can calculate the slope

If x = -5 , what is y?

If y = 2/3, what is x?

Let’s calculate some slopes:

Given the following points, find

The slope of the line joining them
The distance between them
The midpoint of the segment joining them

( 2, - 5) and (-3, 10)

Example C:
4x - 8y - 16 = 0

The first row shows the coordinates of the y intercept.
The second row shows the coordinates of the x intercept.

From this we can calculate the slope

If x = 3/2 , what is y?

If y = 1/4 , what is x?

Now for a bit of review:

Given the line 9x + 3y +18 = 0. Find the following

The slope of the line
The coordinates of the intercepts
The distance between the intercepts
The midpoint of the segment joining the intercepts
If x = -1, what is y?
If y = 2/3, what is x?

Remind me to sketch a graph of this as we go .

The Slope Intercept form for a line	y = mx + b
The slope shows explicitly	m
The y intercept is	( 0, b)

What is the x intercept?

Example

The slope is ________________

The y intercept in coordinate form is ______________________

The x intercept in coordinate form is _____________________

If x = 3/4 , what is y?

If y = 1, what is x?

Point slope equation of a line is:

Using the point slope equation, find an equation of the line through (1, 5) and (2, 6).
What are the intercepts, the slope, the slopes of all lines perpendicular to this line?
What is the y coordinate of the point on the line that has x coordinate 3?
What is the x coordinate of the point on the line that has y coordinate -2?

Parallel lines have the same slope and different y intercepts .
Perpendicular lines have slopes that multiply to -1.

What are the slopes of all lines parallel to the line with y intercept 3 that passes through
(2, -5)? What about all perpendicular lines?

Let’s talk about the points