1. 1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Parallel and Perpendicular Stage 6 - Year 11 Applied Mathematic (Preliminary Extension 1)

2. 2 End of Slide Parallel Lines Two line are parallel if they have the same gradient. y x m1m1 m2m2 m 1 = m 2 Two lines that are parallel. y = mx + b 1 & y = mx + b 2 also ax + by + c 1 = 0 & ax + by + c 2 = 0 m 1 = - abab m 2 = - abab

3. 3 2 = - 3 End of Slide Parallel Lines Example: Show that the two lines are parallel. m = -m = - abab 2 m1 = -m1 = - 3 4 m2 = -m2 = - 6 2x + 3y – 5 = 0 and 4x + 6y -1 =0

4. 4 End of Slide Perpendicular Lines Two line are perpendicular if. y x m1m1 m2m2 m 1 m 2 = -1 or Two lines that are perpendicular. y = mx + b 1 & y = x + b 2 also ax + by + c 1 = 0 & bx - ay + c 2 = 0 m 1 = - abab m 2 = + baba m2 = -m2 = - 1m21m2 - 1m1m

5. 5 End of Slide Perpendicular Gradient Proof y x α β A B C Let segment AB have gradient m 1 = tan α Let segment BC have gradient m 2 = tan β  ACB = 180 - β tan α = cot(180 – β) tan α = - cot β tan α = - 1 tan β cot(180 – β ) = BC AB tan(180 – β ) = AB BC tan α = BC AB m 1 = - 1m2 1m2

6. 6 = 3 2 End of Slide Perpendicular Lines Example: these two lines are perpendicular. m = -m = - abab 2 m1 = -m1 = - 3 6 m2 = -m2 = - -4 2x + 3y – 5 = 0 and 6x - 4y -1 =0