Transcript Parallel and Perpendicular Lines.ppt

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 l1║l2, then m1= m2.
• If m1= m2, then l1║l2.
Parallel and Perpendicular Lines
m1
l1
m2
l2
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 = 2/3x+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 = -2X-4.
m = -2 and the point is (4,-5)
y = mx+b
-5 = -2(4)+b
-5 = -8+b
3=b
y = -2x+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 =1/3x+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 l1┴l2, then m1 ● m2= -1.
• If m1● m2 = -1, then l1┴l2.
Parallel and Perpendicular Lines
l1
l2
m1
m2
6
WRITE THE EQUATION OF THE LINE THAT
PASSES THROUGH (6,-5) AND IS
PERPENDICULAR TO Y = 2X+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 = 2/3X+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