October 3, 2007

Analytic Geometry: Equation and Slope of a Line

Given two points each for line P1P2 and line AB, the equations and slopes of the lines are determined. Through their slopes, it's determined whether the lines are parallel or perpendicular to each other.

ProblemGiven PointsEquations of the LineSlopes of the Line
1P1(7,9) P2(6,3); A(8,5) B(2,6)6x-y-33=0, x+6y-38=0perpendicular lines: m1=-6/-1 m2=1/-6
2P1(4,5) P2(9,8); A(3,2) B(0,7)3x-5y+13=0, 5x+3y-21=0perpendicular lines: m1=3/5 m2=5/-3
3P1(2,6) P2(7,0); A(2,2) B(8,7)6x+5y-42=0, 5x-6y+2=0perpendicular lines: m1=-6/5 m2=5/6
4P1(6,1) P2(2,5); A(5,0) B(9,4)x+y-7=0, x-y-5=0perpendicular lines: m1=1/-1 m2=1/1
5P1(-9,4) P2(9,6); A(12,13) B(3,12)x-9y+45=0, x-9y+105=0parallel lines: m1=1/9 m2=-1/-9
6P1(9,2) P2(5,8); A(3,0) B(9,4)3x+2y-31=0, 2x-3y-6=0perpendicular lines: m1=3/-2 m2=2/3
7P1(1,5) P2(0,2); A(9,1) B(6,2)3x-y+2=0, x+3y-12=0perpendicular lines: m1=-3/-1 m2=1/-3
8P1(2,8) P2(7,5); A(5,4) B(8,9)3x+5y-46=0, 5x-3y-13=0perpendicular lines: m1=-3/5 m2=5/3
9P1(-2,0) P2(4,9); A(6,7) B(10,13)3x-2y+6=0, 3x-2y-4=0parallel lines: m1=3/2 m2=3/2
10P1(5,7) P2(1,1); A(6,5) B(0,9)3x-2y-1=0, 2x+3y-27=0perpendicular lines: m1=-3/-2 m2=2/-3
11P1(-4,9) P2(9,6); A(1,11) B(14,8)3x+13y-105=0, 3x+13y-146=0parallel lines: m1=-3/13 m2=-3/13
12P1(-1,6) P2(9,0); A(10,3) B(0,9)3x+5y-27=0, 3x+5y-45=0parallel lines: m1=-3/5 m2=3/-5
13P1(-6,1) P2(2,9); A(7,12) B(1,6)x-y+7=0, x-y+5=0parallel lines: m1=1/1 m2=-1/-1
14P1(9,7) P2(0,9); A(6,0) B(8,9)2x+9y-81=0, 9x-2y-54=0perpendicular lines: m1=2/-9 m2=9/2
15P1(-2,0) P2(3,7); A(4,7) B(9,14)7x-5y+14=0, 7x-5y+7=0parallel lines: m1=7/5 m2=7/5
16P1(7,1) P2(8,4); A(7,0) B(4,1)3x-y-20=0, x+3y-7=0perpendicular lines: m1=3/1 m2=1/-3
17P1(-3,4) P2(2,0); A(6,0) B(1,4)4x+5y-8=0, 4x+5y-24=0parallel lines: m1=-4/5 m2=4/-5
18P1(-8,3) P2(2,8); A(1,6) B(7,9)x-2y+14=0, x-2y+11=0parallel lines: m1=1/2 m2=1/2
19P1(6,2) P2(7,0); A(6,7) B(8,8)2x+y-14=0, x-2y+8=0perpendicular lines: m1=-2/1 m2=1/2
20P1(-6,6) P2(5,3); A(12,6) B(1,9)3x+11y-48=0, 3x+11y-102=0parallel lines: m1=-3/11 m2=3/-11
21P1(-5,6) P2(1,3); A(6,4) B(12,1)x+2y-7=0, x+2y-14=0parallel lines: m1=-1/2 m2=-1/2
22P1(5,3) P2(9,5); A(3,7) B(5,3)x-2y+1=0, 2x+y-13=0perpendicular lines: m1=1/2 m2=-2/1
23P1(-6,2) P2(4,1); A(14,2) B(4,3)x+10y-14=0, x+10y-34=0parallel lines: m1=-1/10 m2=1/-10
24P1(0,5) P2(3,8); A(6,4) B(7,5)x-y+5=0, x-y-2=0parallel lines: m1=1/1 m2=1/1
25P1(4,3) P2(2,8); A(1,3) B(6,5)5x+2y-26=0, 2x-5y+13=0perpendicular lines: m1=5/-2 m2=2/5
26P1(-6,6) P2(2,1); A(0,5) B(8,0)5x+8y-18=0, 5x+8y-40=0parallel lines: m1=-5/8 m2=-5/8
27P1(-6,1) P2(3,2); A(14,13) B(5,12)x-9y+15=0, x-9y+103=0parallel lines: m1=1/9 m2=-1/-9
28P1(-8,4) P2(4,0); A(6,4) B(3,5)x+3y-4=0, x+3y-18=0parallel lines: m1=-1/3 m2=1/-3
29P1(-4,7) P2(0,4); A(5,11) B(9,8)3x+4y-16=0, 3x+4y-59=0parallel lines: m1=-3/4 m2=-3/4
30P1(7,5) P2(6,2); A(5,8) B(8,7)3x-y-16=0, x+3y-29=0perpendicular lines: m1=-3/-1 m2=-1/3
31P1(-1,3) P2(4,2); A(8,10) B(3,11)x+5y-14=0, x+5y-58=0parallel lines: m1=-1/5 m2=1/-5
32P1(7,2) P2(9,5); A(1,7) B(4,5)3x-2y-17=0, 2x+3y-23=0perpendicular lines: m1=3/2 m2=-2/3
33P1(-2,6) P2(4,1); A(1,7) B(7,2)5x+6y-26=0, 5x+6y-47=0parallel lines: m1=-5/6 m2=-5/6
34P1(-3,9) P2(7,7); A(0,12) B(10,10)x+5y-42=0, x+5y-60=0parallel lines: m1=-1/5 m2=-1/5
35P1(-2,2) P2(3,5); A(6,9) B(1,6)3x-5y+16=0, 3x-5y+27=0parallel lines: m1=3/5 m2=-3/-5
36P1(2,8) P2(4,0); A(1,7) B(9,9)4x+y-16=0, x-4y+27=0perpendicular lines: m1=-4/1 m2=1/4
37P1(2,7) P2(8,3); A(1,1) B(5,7)2x+3y-25=0, 3x-2y-1=0perpendicular lines: m1=-2/3 m2=3/2
38P1(-4,1) P2(1,5); A(10,14) B(5,10)4x-5y+21=0, 4x-5y+30=0parallel lines: m1=4/5 m2=-4/-5
39P1(-4,1) P2(1,4); A(9,7) B(14,10)3x-5y+17=0, 3x-5y+8=0parallel lines: m1=3/5 m2=3/5
40P1(7,6) P2(6,4); A(4,6) B(2,7)2x-y-8=0, x+2y-16=0perpendicular lines: m1=-2/-1 m2=1/-2
41P1(0,4) P2(1,2); A(6,7) B(8,8)2x+y-4=0, x-2y+8=0perpendicular lines: m1=-2/1 m2=1/2
42P1(-9,5) P2(1,0); A(10,8) B(6,10)x+2y-1=0, x+2y-26=0parallel lines: m1=-1/2 m2=1/-2
43P1(9,1) P2(0,9); A(0,0) B(8,9)8x+9y-81=0, 9x-8y-0=0perpendicular lines: m1=8/-9 m2=9/8
44P1(-2,4) P2(8,0); A(9,8) B(14,6)2x+5y-16=0, 2x+5y-58=0parallel lines: m1=-2/5 m2=-2/5
45P1(1,2) P2(2,4); A(4,2) B(6,1)2x-y-0=0, x+2y-8=0perpendicular lines: m1=2/1 m2=-1/2
46P1(0,5) P2(9,3); A(9,11) B(0,13)2x+9y-45=0, 2x+9y-117=0parallel lines: m1=-2/9 m2=2/-9
47P1(3,8) P2(8,2); A(2,2) B(8,7)6x+5y-58=0, 5x-6y+2=0perpendicular lines: m1=-6/5 m2=5/6
48P1(2,2) P2(1,4); A(3,0) B(5,1)2x+y-6=0, x-2y-3=0perpendicular lines: m1=2/-1 m2=1/2
49P1(7,8) P2(0,3); A(8,2) B(3,9)5x-7y+21=0, 7x+5y-66=0perpendicular lines: m1=-5/-7 m2=7/-5
50P1(0,7) P2(4,0); A(2,2) B(9,6)7x+4y-28=0, 4x-7y+6=0perpendicular lines: m1=-7/4 m2=4/7