Upload
lucy-berry
View
218
Download
4
Embed Size (px)
Citation preview
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