G)

PARALLEL

& PERPENDICULAR LINES:

Note:

The

symbol

for

parallel

is

ll

and

for

perpendicular

is I.

Note:

Parallel

lines

have

equal

slopes.

Note:

Perpendicular

lines have negative reciprocal

slopes

,

i.e., if

one is 2,

the other

is

-%.

Example:

Write an equation

of the

line I to the

line

2x-357

andpassing tluough the

point (-2,5).

Solution:

Finding

the

slope

of 2x-3y7

by

solving for

y

,

we

ge!

2x-7:3y+ (213)*7

/3

:

y

+11126

Since

we want a

I line,

the slope we

need is -3/2.

Norna using

point-slope

form

with the

given

poinf"

we

get

y-5

:

(-312)(x+2).

You

may leave

the equation this

way.

Note:

If

you

wanted a

line

parallel

to the

grven

line

instead,

your

answer

would

look like

this:

y-5

:

Ql3)(x+2)

H)

AN

EXAMPLE

OF

FOMULATINGAN EQUANON

FROMA

GEOMETRIC

SITUAIION:

Example:

In

the diagrarrq express the area of the

shaded rectangle in

terms of x.

(3,5

)

The

area

is

a rectangle.

The

area is

the

product

of the

base

&

height.

The

base b is

on the x-axis & is 5-x.

The

height

is the

y-value

to

the

line

segment

at x.

So, we need

to find

this

y-value

in

terms

of

x.

(ttl

so,

get

the

equation

of

this

line.

we have

two

points,

(1,1)

&

(3,5)

on this

line.

The

slope is

(5-1)/3-1)=2.

Using

pt-slope

form,

we

have

y-1=2(x-1).

Solving for

y,

we

get, y=lx-1=h.

So,

the area

of

the shaded

rectangle

;5 4=[fi=(5-x)(2x-1)

x

1)

AREA

OF

A

CIRCLE WITH

RADIUS

r: A:

Tcr'

2)

CIRCUMFERENCE OF ACIRCLE

WITH RADIUS

r: C:Znr

3) PERIMETER

OF

ARECTANGLE

WITH LENGTH

L

and WIDTH w:

P:2L+2w

)