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Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)
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Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Dec 29, 2015

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Tamsyn Bailey
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Page 1: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Page 2: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

We will talk about 3 formulas that are used to calculate various pieces of information about pairs of points.

Each formula refers to a set of two points:

(x1, y1) and (x2, y2)

Page 3: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Distance between two points.In general,

x1 x2

y1

y2

A(x1,y1)

B(x2,y2)

Length = x2 – x1

Length = y2 – y1

the formula for Length of AB or Distance between A

and B is

y

x

Page 4: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

The Distance Formula

2 22 1 2 1( ) ( )d x x y y

"The Distance Formula" sung to the tune of "On Top of Old Smokey"

When finding the distanceBetween the two points,Subtract the two x'sThe same for the y's.Now square these two numbers,And find out their sum.When you take the square rootThen you are all done!

Or use three blindMice songhttps://www.youtube.com/watch?v=m_iyBtstjzs

Page 5: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Example• Find the distance between A(4,8) and B(1,12)

2 22 1 2 1distance ( ) ( )x x y y

A (4, 8)

B (1, 12)

2 2distance (1 4) (12 8) 2 2distance ( 3) (4)

distance 9 16 25 5

First identify your x 1 , x 2 , y 1 and y 2

x1 y1 x2 y2

Page 6: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

More examples

• Find the distance between:– A. (2, 7) and (11, 9)

– B. (-5, 8) and (2, - 4)

2 2(9) (2) 85

2 2(7) ( 12) 193

Page 7: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

You try: (2, 2) and (5, -2)

Distance: ________

Page 9: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Midpoint Formula:

2,

21212 yyxx

Page 10: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

The Midpoint Formula

1 2 1 2( , ) ,2 2

x x y yx y

"The Midpoint Formula" sung to the tune of "The Itsy Bitsy Spider"

When finding the midpoint of two points on a graph,Add the two x's and cut their sum in half.Add up the y's and divide 'em by a two,Now write 'em as an ordered pairIt’s the middle of the two.

Or use the midpoint cheerhttps://www.youtube.com/watch?v=pNoOYVZPEAQ

Page 11: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Example• Find the midpoint between A(4,8) and B(1,12)

2 1 2 1midpoint ,2 2

x x y y

A (4, 8)

B (1, 12)

1 4 12 8midpoint ,

2 2

midpoint 5,10

2

First identify your x 1 , x 2 , y 1 and y 2

x1 y1 x2 y2

Page 12: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

More Examples

• Find the midpoint between:

• A) (2, 7) and (14, 9)

• B) (-5, 8) and (2, - 4)

midpoint = 8,8

-3midpoint = , 2

2

Page 13: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

You Try: (2, 2) and (5, -2)

Midpoint: _______

Page 14: Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Now you get to practice. Please complete the handout and turn it end at the end of class.

Thanks, have a great weekend.