Chapter 4: Matrices Lesson 9: Perpendicular Lines Mrs. Parziale

Perpendicular Lines Two lines are perpendicular if and only if they form a angle with each other. The slopes of two lines that are perpendicular to each other are reciprocals of each other. If you multiply the slopes of two perpendicular lines their product is Thus if the slope of l1 = 4 the slope of l2 that is perpendicular to it is =

Theorems: If two lines with slopes m1 and m2 are perpendicular, then m1m2 = -1 and conversely If two lines have slopes m1 and m2 and m1m2 = -1 then the lines are.

Example 1: Line n contains (3, 8) and is perpendicular to line m whose equation is 5x + 4y = 7. Find the equation for line n.

Example 2: Find the slope of the line perpendicular to x = 5. 1) Graph x = 5 2) Graph any line perpendicular to it. What is its slope? 3) What can you conclude about the slope of a line perpendicular to a vertical line? 4) What is the slope of a line perpendicular to a horizontal line?

Examples Write an equation of the line that goes through the given point and is perpendicular to the given line. 1.(6, 1); y = 3x (-1, -7); 3x + 4y = 7

Examples Write an equation of the line that goes through the given point and is perpendicular to the given line. 3. (5, 2 ); x = ( 5, 2); y = 17

5-Minute Check What is the relationship of the slopes for perpendicular lines? True-False: Two lines that have opposite slopes are parallel. Explain how to find the equation of a line, when given the equation of a line perpendicular to it and a point passing through it.