Section 3 1 Parallel and Perpendicular Lines Parallel

Section 3. 1 Parallel and Perpendicular Lines

Parallel Lines – lie on same plane and never intersect Perpendicular Lines – intersects to form a right angle Skew Lines – do not lie on the same plane, never intersects MAP TAP 2003 -2004 Parallel and Perpendicular Lines 2

Parallel Lines o (Algebra Review) Two non-vertical lines are parallel if and only if their slopes are equal. n n If l 1║l 2, then m 1= m 2. If m 1= m 2, then l 1║l 2. m 1 l 1 MAP TAP 2003 -2004 Parallel and Perpendicular Lines m 2 l 2 3

Write the equation of the line that passes through (3, 6) and is parallel to y = 2/3 x+2. m = 2/3 and the point is (3, 6) y = mx+b 6 = 2/3(3)+b 6 = 2+b 4=b y = 2/3 x+4 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 4

Write the equation of the line that passes through (4, -5) and is parallel to y = -2 x-4. m = -2 and the point is (4, -5) y = mx+b -5 = -2(4)+b -5 = -8+b 3=b y = -2 x+3 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 5

Write the equation of the line that passes through (-6, 4) and is parallel to y=1/3 x-1. m=1/3 and the point is (-6, 4) y =1/3 x+6 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 6

Perpendicular Lines (Algebra Review) o Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. n n If l 1┴l 2, then m 1 ● m 2= -1. l 1 If m 1● m 2 = -1, then l 1┴l 2. Slopes are negative reciprocals MAP TAP 2003 -2004 Parallel and Perpendicular Lines m 1 m 2 l 2 7

Write the equation of the line that passes through (6, -5) and is perpendicular to y = 2 x+3. m = -1/2 and the point is (6, -5) y = mx+b -5 = -1/2(6)+b -5 = -3+b -2 = b y = -1/2 x-2 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 8

Write the equation of the line that passes through (6, -7) and is perpendicular to y = 2/3 x+1. m = -3/2 and the point is (6, -7) y = mx+b -7 = -3/2(6)+b -7 = -9+b 2=b y = -3/2 x+2 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 9

Write the equation of the line that passes through (-4, -3) and is perpendicular to y = x+6. m = -1 and the point is (-4, -3) y = -x-7 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 10

What’s going on in this graph? MAP TAP 2003 -2004 Parallel and Perpendicular Lines 11

MAP TAP 2003 -2004 Parallel and Perpendicular Lines 12

Skew Lines skew lines can exist only in three or more dimensions. MAP TAP 2003 -2004 Parallel and Perpendicular Lines 13

Which lines are skew? MAP TAP 2003 -2004 Parallel and Perpendicular Lines 14

What’s going on here? MAP TAP 2003 -2004 Parallel and Perpendicular Lines 15

Which lines are parallel? MAP TAP 2003 -2004 Parallel and Perpendicular Lines 16

Main Idea MAP TAP 2003 -2004 Parallel and Perpendicular Lines 17

MAP TAP 2003 -2004 Parallel and Perpendicular Lines 18

Over head examples In-Class practice problems Homework p 110 -111 #1 -19 & 25 -29 MAP TAP 2003 -2004 Parallel and Perpendicular Lines 19