PARALLEL AND PERPENDICULAR LINES ALGEBRA 2GEOMETRY HIGH SCHOOL

PARALLEL AND PERPENDICULAR LINES ALGEBRA 2/GEOMETRY HIGH SCHOOL

PARALLEL LINES • Two non-vertical lines are parallel if and only if their slopes are equal. • If l 1║l 2, then m 1= m 2. • If m 1= m 2, then l 1║l 2. PARALLEL AND PERPENDICULAR LINES m 1 l 1 m 2 l 2 MAP TAP 2003 -2004 2

WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH (3, 6) AND IS PARALLEL TO Y = 2 X+2 3 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 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 3

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 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 4

WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH (-6, 4) AND IS PARALLEL TO 1 Y= 3 X-1 m=1/3 and the point s (-6, 4) y =1/3 x+6 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 5

PERPENDICULAR LINES Slopes are negative reciprocals • Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. • If l 1┴l 2, then m 1 ● m 2= -1. • If m 1● m 2 = -1, then l 1┴l 2. PARALLEL AND PERPENDICULAR LINES l 1 l 2 m 1 m 2 6

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 x-2 2 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 7

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 x+2 2 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 8

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 PARALLEL AND PERPENDICULAR LINES MAP TAP 2003 -2004 9