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Distance, Midpoint, & Slope

Distance, Midpoint, & Slope

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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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Page 1: Distance, Midpoint,  & Slope

Distance, Midpoint,

&Slope

Page 2: 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:

Page 3: Distance, Midpoint,  & Slope

Example:

Find the distance between (4, -7) and (8, -4)

Page 4: Distance, Midpoint,  & Slope

Try:

Find the distance between (-2, 4) and (7, 0)

Page 5: Distance, Midpoint,  & Slope

Try:

Find the distance between (-7, 1) and (-4, -1)

Page 6: Distance, Midpoint,  & Slope

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)

Page 7: Distance, Midpoint,  & Slope

MidpointThe ___________________ of a segment is the point

that divides the segment into two ___________ segments.

   

A BM

AM MB

Page 8: Distance, Midpoint,  & Slope

Example:

M is the midpoint of . Find the value of x. Then find the measure of EG.

EG

Page 9: Distance, Midpoint,  & Slope

Example

Find the lengths of VM, MW, and VW.

Page 10: Distance, Midpoint,  & Slope

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 =

Page 11: Distance, Midpoint,  & Slope

Example:

Find the midpoint between (6, -2) and (-4, -5)

Page 12: Distance, Midpoint,  & Slope

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)

Page 13: Distance, Midpoint,  & Slope

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?

Page 14: Distance, Midpoint,  & Slope

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( , )

Page 15: Distance, Midpoint,  & Slope

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.

Page 16: Distance, Midpoint,  & Slope

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:

Page 17: Distance, Midpoint,  & Slope

Try

1. Find the slope between (3, -5) and (6, 7) and describe it.

Page 18: Distance, Midpoint,  & Slope

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.