1. Maintaining Mathematical Proficiency Worksheet
Daily Warm Up
Maintaining Mathematical Proficiency Worksheet

2. Equations of Parallel & Perpendicular Lines Notes 3.5
Goals:
Use slope to partition directed line segments
Identify parallel & perpendicular lines
Write equations of parallel & perpendicular lines
Use slope to find the distance from a point to a line.

3. Partitioning a Line Segment
Example 1.
Partitioning a Line Segment
Find the coordinates of point P along the directed line segment AB so that the ratios of AP to PB is 3 to 2.
Ask students “what words are you not sure, or do no understand, in this question?”
DO NOT DO THIS PROBLEM! GO TO NEXT SLIDE

4. A segment that represents moving from point A to point B.
Core Vocabulary
Directed Line Segment
A segment that represents moving from point A to point B.
Simply put…in my own words
Directed Line Segment AB means start at point A and trace the line ending at point B

5. Partitioning a Line Segment
Example 1.
Partitioning a Line Segment
Find the coordinates of point P along the directed line segment AB so that the ratios of AP to PB is 3 to 2.

6. Core Concept Slopes of Parallel Lines
Theorem 3.13
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope.
any two vertical lines are parallel
Given:
So by the slopes of parallel lines theorem
we can conclude…

7. Core Concept Slopes of Perpendicular Lines
Theorem 3.13
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is –1.
a horizontal line & a vertical line are always perpendicular
Given:
So by the slopes of parallel lines theorem
we can conclude…

8. Identifying Parallel & Perpendicular Lines
Example 2.
Identifying Parallel & Perpendicular Lines
Determine which of the lines are parallel & which of the lines are perpendicular.

9. Writing an Equation of a Parallel Line
Example 3.
Writing an Equation of a Parallel Line
Write an equation of the line passing through the point (–1, 1) that is parallel to the line y = 2x – 3

10. Writing an Equation of a Perpendicular Line
Example 4.
Writing an Equation of a Perpendicular Line
Write an equation of the line passing through the point (2,3) that is perpendicular to the line 2x + y = 2

11. Finding the Distance from a Point to a Line
Example 5.
Finding the Distance from a Point to a Line
Find the distance from the point (1,0) to the line y = –x + 3.

12. Practice Extra Practice – In Class Worksheet Hw #18– Big Ideas TB
Pg. 1, 2, 3-7 odd, 8, even, 30, 43