Geometry Notes
Lesson 1.2b
Equations of parallel,
perpendicular lines and
perpendicular bisectors
CGT.5.G.2
Write equations of lines in slopeintercept form and use slope to determine parallel
and perpendicular lines.
Review
□ Slope-intercept form of a line:
y = mx + b
□ Slope of a line:
m = y 2  y1
x2  x1
Example
□ What is the slope and y-intercept of
the line y = ¾ x – 5?
M=¾
b = -5
Review
General form of a line
Ax + By = C
Review
Example:
□ Write the equation 3x – 7y = 14 in
slope-intercept form.
Parallel lines Review
□ The slope of two parallel lines is always
the same
□ What is the slope of the line parallel to
y = -½ x +2?
-1/2
□ What is the slope of the line parallel to
2x + 10y = 20?
-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
Method 1: Slope - Intercept
thru (-8, 3)
y = mx + b
Parallel to 7x – 8y = 16
Method 2: Point - Slope
thru (-8, 3)
y-y1 = m(x-x1)
Parallel to 7x – 8y = 16
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?
two lines that intersect at a right angle
□ The slopes of perpendicular lines are
always Opposite reciprocals
□ What is the slope of the line
perpendicular to y = 2/3 x - 4? -3/2
Example #2:
□ Write the equation of the line
perpendicular to y = -8/9 x – 2 through
the point (8, 3).
Method 1: Slope - Intercept
thru (8, 3)
y = mx + b
Perp. to y = -8/9 x – 2
Method 2: Point - Slope
thru (8, 3)
y-y1 = m(x-x1)
Perp. to y = -8/9 x – 2
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.
2.
3.
4.
Find the midpoint of the segment
Find the slope of the segment
Find the Perpendicular slope
Write the equation using either PointSlope 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