Pre Calc 10 6 5 Perpendicular Lines Perpendicular

Pre Calc 10 6. 5 Perpendicular Lines

Perpendicular Lines: When two lines are perpendicular, they intersect at 90 degrees a Vertical Line is perpendicular to a Horizontal Line The angle between them is 90 degrees

Things that are Perpendicular: Two sides of a right triangle are perpendicular Adjacent sides of a rectangle & square perpendicular The diagonals of a “square” are perpendicular

Properties of Perpendicular Lines When two slopes are perpendicular, they are “negative reciprocals (Flip the number and change the sign!) Ex: Find the negative reciprocal of each number: The product of any number with it’s negative reciprocal is -1 If you multiply two slopes that are “PERPENDICULAR” their product will become -1

Negative Reciprocal Slopes When two slopes are “Negative Reciprocal” they are perpendicular. C (8, 6) A (-8, 7) Negative Reciprocal Lines AB & BC are because their slopes are “Negative Reciprocals” B (-1, -2) When you multiply the slopes of AB & BC, the product is -1

Ex: Given the points, check if the two lines are perpendicular A (-7, 8) Find the slope of both lines: B (-2, 5) C (-3, -4) D (3, 6) Multiply the slopes of AB & CD. If the product is -1, then the lines are perpendicular The lines are perpendicular!

Ex: Given the points, check if the two lines are perpendicular Find the slope of both lines: B (-5, 4) C (-1, 2) A (-10, -3) D (4, -5) Multiply the slopes of AB & CD. If the product is -1, then the lines are perpendicular The lines are NOT perpendicular!

Ex: Given the vertices of ABC, check if it is a right triangle? IF ABC is a right triangle, then two sides must be perpendicular B (-2, 5) Find the slope of all sides: A (-6, -2) ABC is a Right Triangle! C (1, -6) Check if any slopes are “Negative Reciprocal”

Challenge Problem: The slopes of two perpendicular lines are given, what is the value of k? If the two slopes are perpendicular, then the product will be -1. Solve for “k”

Challenge Problem: ABC is an Isosceles Right Triangle. The Hypotenuse AB is on the X-axis. Find the coordinates of “C” Point “C” is unknown, and it makes an Isosceles Right Triangle CCC (? , ? )) (-1, 5 (? , ? ) Since it’s anofisosceles The product the two triangle, sides must slopes is opposite -1 (Perpendicular) be equal. Point “C” must be in the middle between “A” & “B” Solve for “x” A (-6, 0) Since it’s also a Right triangle, the two sides must be perpendicular. B (4, 0) The Slope of AC & CB must be coordinates of “C” is (-1, 5) negative reciprocal

Homework: Pp 187 #1, 3, 7, 11, 16, 19, 21,