angle between 2 lines question (1 Viewer)

[karina611]

can anyone help me out with this question:

find two possible values of m if the lines 2x + y - 5 = 0 and y = mx + 1 intersect at an angle of 45°

 

[joeyann]

did you use the angle between two lines equation?

tan θ = |m1-m2| / 1+m1m2
tan 45 = |2 - m| / 1+2m
2-m = 1+2m
3m = 1
m=1/3

but i'm not sure how to get two values of m.. maybe the absolute value in the equation gives you two...

 

[watatank]

did you use the angle between two lines equation?

tan θ = |m1-m2| / 1+m1m2
tan 45 = |2 - m| / 1+2m

Since you are working with absolute values...

2-m = 1+2m OR -2+m = 1+2m
3m = 1 OR m= -3
m=1/3 OR -3

Fixed.

 

[SoulSearcher]

Also solve for when (2-m) is negative, i.e. 1+2m = m-2

 

[Trebla]

did you use the angle between two lines equation?

tan θ = |m1-m2| / 1+m1m2
tan 45 = |2 - m| / 1+2m
2-m = 1+2m
3m = 1
m=1/3

but i'm not sure how to get two values of m.. maybe the absolute value in the equation gives you two...

That's right, the third line should have been |2 - m| = 1 + 2m because we don't know if 2 - m is positive or negative. So we consider two cases:

Case 1:
2 - m = 1 + 2m
.: m = 1/3

Case 2:
- (2 - m) = 1 + 2m
m - 2 = 1 + 2m
.: m = -3

 

[Robert1961]

2x + y – 5 = 0

becomes

y = -2x + 5

Let m1 = -2 & m2 = m


tan(acute angle between 2 lines) = Absolute Value [(m2 - m1)/(1 + m1. m2)]

tan(45deg) = 1 = Absolute Value [(m - -2)/(1 + -2. m)]

1 = Absolute Value [(m + 2)/(1 - 2m)]

1 = Absolute Value (m + 2) / Absolute Value (1 – 2m)

Absolute Value (1 – 2m) = Absolute Value (m + 2)

1 – 2m = m + 2 or 1 – 2m = -m – 2

-1 = 3m or 3 = m

m = -1/3 or m = 3