PARALLEL AND PERPENDICULAR LINES ALGEBRA 2/GEOMETRY HIGH SCHOOL.
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Transcript of PARALLEL AND PERPENDICULAR LINES ALGEBRA 2/GEOMETRY HIGH SCHOOL.
PARALLEL AND PERPENDICULAR
LINESALGEBRA 2/GEOMETRY
HIGH SCHOOL
PARALLEL LINES
MAP TAP 2003-2004
Parallel and Perpendicular Lines 2
• 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.
l1 l2
m1 m2
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+b6 = 2/3(3)+b6 = 2+b4 = b
y = 2/3x+4 MAP TAP 2003-2004
Parallel and Perpendicular Lines
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+b3 = b
y = -2x+3MAP TAP 2003-2004
Parallel and Perpendicular Lines 4
WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH (-6,4) AND IS
PARALLEL TO Y= 1 X-1
3m=1/3 and the point s (-6,4)
y =1/3x+6MAP TAP 2003-2004
Parallel and Perpendicular Lines 5
PERPENDICULAR LINES
Parallel and Perpendicular Lines 6
• 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.l1
l2
m2m1
Slopes are negative reciprocals
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
MAP TAP 2003-2004
Parallel and Perpendicular Lines 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+b2 = b
y = -3 x+2 2
MAP TAP 2003-2004
Parallel and Perpendicular Lines 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-7MAP TAP 2003-2004
Parallel and Perpendicular Lines 9