Maths Help (Co-ordinate geometry)

The__Malteser · 1 Oct 2012 at 19:17

In triangle ABC, A has co-ordinates (7,8). The mid-point of BC is D(4,2). The perpendicular bisector of BC meets AB at E(3,4).
(i) Find the equation of AE.
(ii) Find the co-ordinates of B.

I am normally good at co-ordinate geometry, but I can't seem to solve the second part.

I did the first part (answer: y = x + 1)

The second part is where I am stuck. I out of ideas. I concluded that BD = DC (D is the mid-point) & BDE is 90deg, because the bisector is perpendicular. I know B is on the line found above, but I still can't figure it out lol.

here is a diagram to help you out:

Its probably something small, but I can't get it! That's what frustrates me!

Any help is appreciated.

AshD93 · 1 Oct 2012 at 19:26

I can't be bothered to work it out nor do I know if this will work as it's been a long day but...

Work out the line equation for ED. You know the line equation for BEA.

Do the tangent of ED or whatever it's called to give you the equation of BDC.

Then do simultaneous equations.

Edit:

I'm too nice.

X = -2, Y = -1 (I rushed it so if its wrong...)

btw, the gradient for ED is -2 so the gradient for BDC is 1/2.

That gives you the equations

y = x + 1

2y = x

The__Malteser · 1 Oct 2012 at 19:45

Done! Thanks. It has more parts to the question but I was stuck on II. Thanks a lot

AshD93 · 1 Oct 2012 at 19:50

You're welcome. Post if you need more help.