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Distance, Midpoint, & Slope. d =. d =. d =. The Distance Formula. Find the distance between (-3, 2) and (4, 1). d =. Example:. x 1 = -3, x 2 = 4, y 1 = 2 , y 2 = 1. Exa mple:. Find the distance between (4, -7) and (8, -4). Try :. - PowerPoint PPT Presentation
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Distance, Midpoint,
&Slope
The Distance Formula
Find the distance between (-3, 2) and (4, 1) x1 = -3, x2 = 4, y1 = 2 , y2 = 1
2 2(4 3) (1 2) d = 2 2(7) ( 1) 49 1 d =
50 or 5 2 or 7.07d =
d = 2 2
2 1 2 1( ) ( )x x y y
Example:
Example:
Find the distance between (4, -7) and (8, -4)
Try:
Find the distance between (-2, 4) and (7, 0)
Try:
Find the distance between (-7, 1) and (-4, -1)
Plot the points J, K, L, and M. Draw a segment from J to K and another segment from L to M. Decide if JK and LM are congruent.
J (-4, 0) K (4, 8) L (-4, 2) M (3, -7)
MidpointThe ___________________ of a segment is the point
that divides the segment into two ___________ segments.
A BM
AM MB
Example:
M is the midpoint of . Find the value of x. Then find the measure of EG.
EG
Example
Find the lengths of VM, MW, and VW.
Midpoint Formula
1 2 1 2,2 2
x x y y
42
,92
= 2,
92
M =
2 62
,5 4
2
M =
Find the midpoint between (-2, 5) and (6, 4) x1 = -2, x2 = 6, y1 = 5, and y2 = 4
Example:
Midpoint =
Example:
Find the midpoint between (6, -2) and (-4, -5)
Try: Find the midpoint of these two points.
3. A (4, 2) B ( 1, -3)
4. R (-3, -2), S (-1, 0)
5. P(-8, -7), Q( 11, 5)
Finding the missing Endpoint
The midpoint of is M (2,1).
One endpoint is J (1,4). How do you find the
coordinate of K?
Examples:
1. Find endpoint S given that M is the midpoint of RS M (5,3) R (6, -2) S( , )
2. Find endpoint S given that M is the midpoint of RS
M (-2,0) R (-4, -3) S( , )
Describing Lines
Lines that have a positive slope rise from left to right.
Lines that have a negative slope fall from left to right.
Lines that have no slope (the slope is undefined) are vertical.
Lines that have a slope equal to zero are horizontal.
SlopeDefinition: The ratio of vertical change (rise) to horizontal change (run)
between any two points on the line.
Ex: Find the slope of the line containing (-2, 8) and (5, -6).
Solution:
Try
1. Find the slope between (3, -5) and (6, 7) and describe it.
Some More Examples
1. Find the slope between (4, -5) and (3, -5) and describe it.
Since the slope is zero, the line must be horizontal.
5 54 3
01
0m =
2. Find the slope between (3,4) and (3,-2) and describe the line. 4 2
3 3
60
m =
Since the slope is undefined, the line must be vertical.