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

[Natasha1]

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

 

[Ray Vickson]

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]

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

 

[Natasha1]

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

Maybe you could help me with my question on frustum https://www.physicsforums.com/threads/find-an-expression-for-the-height-of-the-frustum.967669/ :)