# Find an equation of a line of symmetry in the form px+qy = r

## Homework Statement

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.

## The Attempt at a Solution

Would the equation of the line of symmetry of triangle ABC be y = -3/2 x + c (as it's perpendicular to y=2/3x + 4)

So as it goes through A (4,37) we get y = -3/2 x + 43

How on earth do you get the form px + qy = r

Last edited:

Ray Vickson
Homework Helper
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## Homework Statement

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.

## The Attempt at a Solution

Would the equation of the line of symmetry of triangle ABC be y = -3/2 x + c (as it's perpendicular to y=2/3x + 4)

So as it goes through A (4,37) we get y = -3/2 x + 43

How on earth do you get the form px + qy = r

Doesn't the equivalent form ##(3/2) x + 1 y = 43## count? What about ##3 x + 2 y = 86?##

Natasha1 and Phylosopher
Ray, you are a star! Thanks so much :)