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Can anyone help me with this GCSE maths question?

Hi everyone! I'm doing a past paper and I'm stuck on this one:
ABC is an isosceles triangle such that AB = AC, A has coordinates (4,37), B and C lie on the line with equation 3y = 2x + 12.
Find an equation of the line of symmetry of triangle ABC.
Give your answer in the form px + qy = r where p, q and r are integers. Show clear algebraic working.
Original post by horse&ponylover
Hi everyone! I'm doing a past paper and I'm stuck on this one:
ABC is an isosceles triangle such that AB = AC, A has coordinates (4,37), B and C lie on the line with equation 3y = 2x + 12.
Find an equation of the line of symmetry of triangle ABC.
Give your answer in the form px + qy = r where p, q and r are integers. Show clear algebraic working.


Can you think of how the line of symmetry might relate to the line joining B and C?
Original post by ghostwalker
Can you think of how the line of symmetry might relate to the line joining B and C?

Is it the midpoint?
Original post by ghostwalker
Can you think of how the line of symmetry might relate to the line joining B and C?


I've got that the equation of BC = y = 2/3x + 4, but how do I find the midpoint of that?
Original post by horse&ponylover
Is it the midpoint?


Well, yes, it's the midpoint of BC, but you don't know the coordinates of B and C, so you can't use that.

How do the two lines, the one joining BC and the line of symmetry, relate? You might find a diagram of an isosceles triangle useful to look at.
Original post by ghostwalker
Well, yes, it's the midpoint of BC, but you don't know the coordinates of B and C, so you can't use that.

How do the two lines, the one joining BC and the line of symmetry, relate? You might find a diagram of an isosceles triangle useful to look at.

They're perpendicular! So the gradient of the line of symmetry = -3/2?
Original post by horse&ponylover
They're perpendicular! So the gradient of the line of symmetry = -3/2?


Bingo! Can you finish from there?
Ok, I think I have the answer but I'm not quite sure how to give it in the form px + qy = r. I have for the equation of the line of symmetry: y = -3/2x + 43, is that right?
Original post by horse&ponylover
Ok, I think I have the answer but I'm not quite sure how to give it in the form px + qy = r. I have for the equation of the line of symmetry: y = -3/2x + 43, is that right?


Yes, that's correct so far.

The only remaining problem is to rearrange into the form they want and get rid of the "/2". Simpliest way is just to multiply everything by 2, and rearrange.
Original post by ghostwalker
Yes, that's correct so far.

The only remaining problem is to rearrange into the form they want and get rid of the "/2". Simpliest way is just to multiply everything by 2, and rearrange.


3x + 2y = 86 ! Thank you for your help :h:
Original post by horse&ponylover
Hi everyone! I'm doing a past paper and I'm stuck on this one:
ABC is an isosceles triangle such that AB = AC, A has coordinates (4,37), B and C lie on the line with equation 3y = 2x + 12.
Find an equation of the line of symmetry of triangle ABC.
Give your answer in the form px + qy = r where p, q and r are integers. Show clear algebraic working.


Go to this site - https://reptondubaimathematics.files.wordpress.com/2019/03/june-18-1h-and-2h-worked-solutions.pdf
And check out page 12. It has the answer. See if you understand it :smile:
Original post by fatheha123
Go to this site - https://reptondubaimathematics.files.wordpress.com/2019/03/june-18-1h-and-2h-worked-solutions.pdf
And check out page 12. It has the answer. See if you understand it :smile:


Thank you! I got it right :smile:

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