Transcript 1.2B Writing Equations of Lines LESSON

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