1. Equations of parallel, perpendicular lines and perpendicular bisectors
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.

2. Review
Slope-intercept form of a line:
Slope of a line:
y = mx + b
m =

3. Example What is the slope and y-intercept of the line y = ¾ x – 5?
M = ¾ b = -5

4. Review
Ax + By = C
General form of a line

5. Review
Example:
Write the equation 3x – 7y = 14 in slope-intercept form.

6. 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

7. 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

8. Method 1: Slope - Intercept
thru (-8, 3) Parallel to 7x – 8y = 16 y = mx + b

9. Method 2: Point - Slope
thru (-8, 3) Parallel to 7x – 8y = 16 y-y1 = m(x-x1)

10. 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

11. 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

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

13. Method 1: Slope - Intercept
thru (8, 3) Perp. to y = -8/9 x – 2 y = mx + b

14. Method 2: Point - Slope thru (8, 3) Perp. to y = -8/9 x – 2
y-y1 = m(x-x1)

15. 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

16. Perpendicular Bisectors
What is a perpendicular bisector?
a line or segment that is perpendicular to a segment and intersects it at its midpoint

17. Steps for finding the Perpendicular Bisector of a Segment
Find the midpoint of the segment
Find the slope of the segment
Find the Perpendicular slope
Write the equation using either Point-Slope or Slope-Intercept methods

18. Example #3:
Write the equation of the perpendicular bisector of the segment with the two given endpoints: (1, 0) and (-5, 4)

19. 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