Question

Two straight lines are perpendicular to each other. The sum of their slopes is equal to 1. What is the difference of their slopes ?
Two straight lines are perpendicular to each other. The sum of their slopes is equal to 1. What is the difference of their slopes ?
@Mathematics

Answer 1

the difference of the slopes is \[\pm \sqrt{5}\]

Answer 2

Thanks, Arnab.

Answer 3

Is there a visual way of getting to the answer, than the quadratic ?

Answer 4

yeah, of course. i am explaining

Answer 5

take the slopes m1 and m2
then m1*m2=-1
m1+m2=1
so, m1-m2=\[\pm \sqrt{(m1+m2)^{2}-4m1m2}=\pm \sqrt{5}\]

Answer 6

m1*m2=-1
M1+m2=1
.

m1*m2=-1 (because perpendicular)
m1+m2=1 (sum of gradients = 1)
M1=-1/m2
M1+m2-1=0
m1+1/m2=0
simultaneous equations using subsitituion
m1-m1+m2-1-1/m2=0
m2-1/m2-1=0
m2^2-m2/m2+1=0 (times through by m2
m2^2-1+1=0
M2=0
How did you get +-sqrt5?

Answer 7

@payals, u got it?

Answer 8

Yes, thanks. Would be even better if there is some visual intuition to it.

Answer 9

@ullere, i cant get ur process

Answer 10

maybe it will be better if u take help of equation button :)

Answer 11

sorry it might be clearer if I use x and y

x*y=-1 (perpendicular lines)
x+y=1 (sum of lines = 1)
first equation
x*y=-1 (divde both sides by y
X*y/y=-1/y,
x=-1/y (add 1/y to both sides)
x + 1/y = 0

second equation

x+y=1 (subtract 1 from both sides)
x+y-1=0

so now I use substitution to simultaneously solve the equations

x+1/y = 0
x+y+1 = 0
x+y+1=x+1/y (subtract x+1/y from both sides

x +y +1 - x - 1/y = 0

y+1 -1/y = 0 (multiply equation y)
=y^2+y-1=0

b2-4ac = 5

yeah I must have messed up last time, your answer is right I reckon.