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