Can anyone help me with this GCSE maths question? Watch

horse&ponylover
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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.
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ghostwalker
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(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?
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horse&ponylover
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(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?
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horse&ponylover
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(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?
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ghostwalker
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(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.
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horse&ponylover
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(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?
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ghostwalker
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(Original post by horse&ponylover)
They're perpendicular! So the gradient of the line of symmetry = -3/2?
Bingo! Can you finish from there?
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horse&ponylover
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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?
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ghostwalker
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(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.
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horse&ponylover
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(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
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fatheha123
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(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...-solutions.pdf
And check out page 12. It has the answer. See if you understand it
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horse&ponylover
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(Original post by fatheha123)
Go to this site - https://reptondubaimathematics.files...-solutions.pdf
And check out page 12. It has the answer. See if you understand it
Thank you! I got it right
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