# 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

simplify -2^{0}

**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

Distance

Midpoint

Equation of line containing them

Slope of all lines parallel

Slope of all lines perpendicular

**1.3 Graphing Equations**

The x intercept is

to solve for the x intercept (s): 0 = f(x)

The y intercept is

to solve for the y intercept (s): f(0)

evaluation:

explore:

x = 0

x = -1 or 1

x = 2

solve for the x intercept(s):

The domain is

The range is

Be sure to review evaluation:

Sample attendance popper questions are on my website.

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