another co-ord geo qs (1 Viewer)

[Smeegen999]

find the acute angle between the straight lines with equations

3x - y = 5

2x - 4y + 1 = 0

thanks!!!

 

[Mark576]

tan Θ = |m₁-m₂|/|1+m₁m₂|, where Θ is the angle between two lines with gradients m₁ and m₂.

 

[Smeegen999]

could u explain 2 me how this works :S

 

[me121]

well this works by calculating the angle each line makes with zero degrees. i.e. the line horizontal from the origin.

So if you change the form,
3x - y = 5
into
y = 3x -5
i.e. gradient is 3.

and for the second one,
2x - 4y + 1 = 0
4y=2x+1
y=1/2 x + 1/4
i.e. gradient is 1/2.

Now we know that tan^-1 gradient = angle the line makes with the +x axis.

so to calculate the angle between the lines we can subtract the angle of one of the lines with the angle of the other line. if this gives a negative answer, change the order of the terms. however there will always be two angles, you can calculate the other one by using 180 - angle.

this is how you would derive the formula. and as a side note, even for my hsc, i never memorised the formula, i just used the above method.

EDIT: This is a 3unit topic. You will not be examined on it in 2U. By the looks of your profile, you only do 2U.

 

[Mark576]

3x - y = 5 => m₁ = 3
2x - 4y + 1 = 0 => m₂ = 1/2
∴ tan Θ = |3-(1/2)|/|1+(3/2)| = 1
Θ = tan^-11 = 45^o

Does that help?

 

[Smeegen999]

well this works by calculating the angle each line makes with zero degrees. i.e. the line horizontal from the origin.

So if you change the form,
3x - y = 5
into
y = 3x -5
i.e. gradient is 3.

and for the second one,
2x - 4y + 1 = 0
4y=2x+1
y=1/2 x + 1/4
i.e. gradient is 1/2.

Now we know that tan^-1 gradient = angle the line makes with the +x axis.

so to calculate the angle between the lines we can subtract the angle of one of the lines with the angle of the other line. if this gives a negative answer, change the order of the terms. however there will always be two angles, you can calculate the other one by using 180 - angle.

this is how you would derive the formula. and as a side note, even for my hsc, i never memorised the formula, i just used the above method.

EDIT: This is a 3unit topic. You will not be examined on it in 2U. By the looks of your profile, you only do 2U.

oh i see, its a 3 unit topic - that explains it! I was stressing out majorly because I've never seen that formula b4 lol. thanks 4 clearing that up. That qs was in my stupid 2U textbook!

 

[nekobutterfly]

which maths book do you have?

 

[Smeegen999]

maths in focus - margaret grove