Geometry Notes Lesson 1.2b

Equations of parallel, perpendicular lines and perpendicular bisectors

CGT.5.G.2 Write equations of lines in slope-intercept form and use slope to determine

parallel and perpendicular lines.

Review

□Slope-intercept form of a line:

□Slope of a line:

y = mx + b

m = 12

12

xx

yy

Example

□What is the slope and y-intercept of the line y = ¾ x – 5?

M = ¾ b = -5

General form of a line

Ax + By = C

Review

Example: □Write the equation 3x – 7y = 14 in

slope-intercept form.

Review

Parallel lines Review

□The slope of two parallel lines is always

□What is the slope of the line parallel to y = -½ x +2?

□What is the slope of the line parallel to 2x + 10y = 20?

the same

-1/2

-1/5

Writing Equations Example #1

□Write the equation of the line parallel to 7x – 8y = 16 that goes through the point (-8, 3).

Two methods: □Slope-Intercept Method□Point-Slope Method

thru (-8, 3) Parallel to 7x – 8y = 16

y = mx + b

Method 1: Slope - Intercept

thru (-8, 3) Parallel to 7x – 8y = 16

y-y1 = m(x-x1)

Method 2: Point - Slope

Now You Try…

□Write the equation of the line parallel to the given line through the given point: 11x + 5y = 55 ; (-5, 12)

Y = -11/5x + 1

Perpendicular Lines

□What are perpendicular lines?

□The slopes of perpendicular lines are always

□What is the slope of the line perpendicular to y = 2/3 x - 4?

two lines that intersect at a right angle

Opposite reciprocals

-3/2

Example #2:

□Write the equation of the line perpendicular to y = -8/9 x – 2 through the point (8, 3).

thru (8, 3) Perp. to y = -8/9 x – 2

y = mx + b

Method 1: Slope - Intercept

Method 2: Point - Slope

thru (8, 3) Perp. to y = -8/9 x – 2

y-y1 = m(x-x1)

Now You Try…

□Write the equation of the line perpendicular to the given line through the given point. y = 3/7 x – 1 ; (3, -10)

Y = -7/3x - 3

Perpendicular Bisectors

□What is a perpendicular bisector? □a line or segment that is

perpendicular to a segment and intersects it at its midpoint

Steps for finding the Perpendicular Bisector of a

Segment 1. Find the midpoint of the

segment2. Find the slope of the segment3. Find the Perpendicular slope4. Write the equation using either

Point-Slope or Slope-Intercept methods

Example #3:

□Write the equation of the perpendicular bisector of the segment with the two given endpoints: (1, 0) and (-5, 4)

Now You Try…

□Write the equation of the perpendicular bisector of the segment with the two given endpoints: (-2, -12) and (-8, -2)

Y = 3/5x - 4