FORMULASFORMULAS

Moody Mathematics

Let’s review how to “set Let’s review how to “set up” a formula with the up” a formula with the numbers in their correct numbers in their correct places:places:

Moody Mathematics

Find the slope of the line Find the slope of the line that passes through (-2, that passes through (-2, 44) ) and (6,and (6,11):):

2 1

2 1x

y y

x

Moody Mathematics

Find the slope of the line Find the slope of the line that passes through (-2, that passes through (-2, 44) ) and (6,and (6,11):):

2 1

4 1

x x

Moody Mathematics

Find the slope of the line Find the slope of the line that passes through (that passes through (-2-2, 4) , 4) and (and (66,1):,1):

2 1

4 1

x x

Moody Mathematics

Find the slope of the line Find the slope of the line that passes through (that passes through (-2-2, 4) , 4) and (and (66,1):,1):

4

2

1

6

Moody Mathematics

Find the slope of the line Find the slope of the line that passes through (-2, 4) that passes through (-2, 4) and (6,1):and (6,1):

4 1 3

2 6 8

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (3,4) and segment joining (3,4) and (-5,-6).(-5,-6).

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (segment joining (33,4) and ,4) and ((-5-5,-6).,-6).

1 2 1 2,2 2

yx x y

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (segment joining (33,4) and ,4) and ((-5-5,-6).,-6).

1 23

2

5,

2

y y

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (3,segment joining (3,44) and ) and (-5(-5,-6,-6).).

1 23 5,

2 2

y y

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (3,segment joining (3,44) and ) and (-5(-5,-6,-6).).

3

2

65,

2

4

Moody Mathematics

Find the midpoint of the Find the midpoint of the segment joining (3,4) and segment joining (3,4) and (-5,-6).(-5,-6).

3 5 4 6 2 2, ,

2 2 2 2

( 1, 1)

Moody Mathematics

Find the distance between Find the distance between (-2,-6) and (4, 2): (-2,-6) and (4, 2):

Moody Mathematics

Find the distance between Find the distance between ((22,-6) and (,-6) and (-4-4, 2): , 2):

2

1

2

2 2 1d x x y y

Moody Mathematics

Find the distance between Find the distance between ((22,-6) and (,-6) and (-4-4, 2): , 2):

2 2

2 14 2d y y

Moody Mathematics

Find the distance between Find the distance between (2(2,-6,-6) and (-4, ) and (-4, 22): ):

2

2 1

24 2d y y

Moody Mathematics

Find the distance between Find the distance between (2(2,-6,-6) and (-4, ) and (-4, 22): ):

2 24 2 2 6d

Moody Mathematics

Find the distance between Find the distance between (2,-6) and (-4, 2): (2,-6) and (-4, 2):

2 2

2 2

4 2 2 6

( 6) (8)

d

Moody Mathematics

Find the distance between Find the distance between (2,-6) and (-4, 2): (2,-6) and (-4, 2):

2 2

2 2

4 2 2 6

( 6) (8) 36 64

d

Moody Mathematics

Find the distance between Find the distance between (2,-6) and (-4, 2): (2,-6) and (-4, 2):

2 2

2 2

4 2 2 6

( 6) (8) 36 64

100

d

Moody Mathematics

Find the distance between Find the distance between (2,-6) and (-4, 2): (2,-6) and (-4, 2):

2 2

2 2

4 2 2 6

( 6) (8) 36 64

10100

d

Moody Mathematics

Identify what each Identify what each of the following of the following formulas is used formulas is used for:for:

Moody Mathematics

1

2A b h

Moody Mathematics

1

2A b h

Area of a TriangleArea of a Triangle

Moody Mathematics

2 1

2 1

y y

x x

Moody Mathematics

2 1

2 1

y y

x x

The Slope of a lineThe Slope of a line

Moody Mathematics

2( )P l w

Moody Mathematics

2( )P l w Perimeter of a RectanglePerimeter of a Rectangle

Moody Mathematics

2A s

Moody Mathematics

2A s Area of a SquareArea of a Square

Moody Mathematics

2 2 2a b c

Moody Mathematics

2 2 2a b c Pythagorean Theorem– Pythagorean Theorem– Used to find a missing side Used to find a missing side of a right triangle.of a right triangle.

Moody Mathematics

1 2 1 2,2 2

x x y y

Moody Mathematics

1 2 1 2,2 2

x x y y

The Midpoint of a segmentThe Midpoint of a segment

Moody Mathematics

2A r

Moody Mathematics

2A r Area of a CircleArea of a Circle

Moody Mathematics

4P s

Moody Mathematics

4P s Perimeter of a SquarePerimeter of a Square

Moody Mathematics

2 2

2 1 2 1d x x y y

Moody Mathematics

2 2

2 1 2 1d x x y y The distance formula—for finding The distance formula—for finding the length of a segment.the length of a segment.

Moody Mathematics

2C r

Moody Mathematics

2C r The Circumference of a circleThe Circumference of a circle

Moody Mathematics

Lines that are Lines that are parallel, parallel, perpendicular, or perpendicular, or neither:neither:

Moody Mathematics

Describe the relationship:Describe the relationship:2

132

63

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

26

2

31

3

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

26

2

31

3

y x

y x

These lines are Parallel.These lines are Parallel.

Moody Mathematics

Describe the relationship:Describe the relationship:2

432 1

3 4

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

4

4

2

32

3

1

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

4

4

2

32

3

1

y x

y x

These lines are nothing These lines are nothing special.special.

Moody Mathematics

Describe the relationship:Describe the relationship:

5 1

16

5

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

15

16

5

y x

y x

Moody Mathematics

Describe the relationship:Describe the relationship:

15

16

5

y x

y x

These lines are perpendicular.These lines are perpendicular.

Moody Mathematics

Now we will practice Now we will practice the various formulas the various formulas in a direct and an in a direct and an indirect way:indirect way:

Moody Mathematics

Find the area of a rectangle Find the area of a rectangle with length of 4 in. and with length of 4 in. and width of 3 in.width of 3 in.

Moody Mathematics

Find the area of a rectangle Find the area of a rectangle with length of 4 in. and with length of 4 in. and width of 3 in.width of 3 in.

A l w

Moody Mathematics

Find the area of a rectangle Find the area of a rectangle with length of 4 in. and with length of 4 in. and width of 3 in.width of 3 in.

4 3

12 . .

A l w

A

A sq in

Moody

Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of 24 sq. in. and a with Area of 24 sq. in. and a length of 8 in.length of 8 in.

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of with Area of 2424 sq. in. and a sq. in. and a length of 8 in.length of 8 in.

A l w

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of with Area of 2424 sq. in. and a sq. in. and a length of 8 in.length of 8 in.

24 l w

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of 24 sq. in. and a with Area of 24 sq. in. and a length of length of 88 in. in.

24 wl

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of 24 sq. in. and a with Area of 24 sq. in. and a length of length of 88 in. in.

24 8 w

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of 24 sq. in. and a with Area of 24 sq. in. and a length of 8 in.length of 8 in.

24 8

8 8

w

Moody Mathematics

Find the width of a rectangle Find the width of a rectangle with Area of 24 sq. in. and a with Area of 24 sq. in. and a length of 8 in.length of 8 in.

3 w

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

2( )P l w

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of with a Perimeter of 2020 in. and in. and a width of 5 in.a width of 5 in.

2( )P l w

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of with a Perimeter of 2020 in. and in. and a width of 5 in.a width of 5 in.

2( )20 l w

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of a width of 55 in. in.

20 2( )wl

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of a width of 55 in. in.

20 2( 5)l

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

20 2( 5)l

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

20 2 10l

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

20 2 10

10 10

l

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

10 2l

Moody Mathematics

Find the length of a rectangle Find the length of a rectangle with a Perimeter of 20 in. and with a Perimeter of 20 in. and a width of 5 in.a width of 5 in.

10 2

5

l

l

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 628 m.with circumference of 628 m.

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

2C r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of with circumference of 62.862.8 m. m.

2C r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of with circumference of 62.862.8 m. m.

262.8 r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

62.8 2 r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

62.8 2 (3.1 )4 r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

62.8 2 (3.1 )4 r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

6.2862.8

62.8

6.28

r

r

Moody Mathematics

Find the radius of the circle Find the radius of the circle with circumference of 62.8 m.with circumference of 62.8 m.

62.8

6.2810

r

r

Moody Mathematics

The EndThe End

Moody Mathematics