You are Here: Home >< Maths

# Straight Lines watch

1. The points A(-2, 3) and C(9, 4) are two vertices of an isosceles triangle ABC in which AC = BC. The side AB lies on x+y=1. Find coordinates of B.

I’ve tried so much - I’ve worked out the length of AC and got root122, worked out the equation of AC as 11y=x+35. I’ve also tried letting B be (a,b) and working out an equation for the line BC and finding the equation where x+y=1 intersects this.

Am I missing something?
2. (Original post by danielwinstanley)
The points A(-2, 3) and C(9, 4) are two vertices of an isosceles triangle ABC in which AC = BC. The side AB lies on x+y=1. Find coordinates of B.

I’ve tried so much - I’ve worked out the length of AC and got root122, worked out the equation of AC as 11y=x+35. I’ve also tried letting B be (a,b) and working out an equation for the line BC and finding the equation where x+y=1 intersects this.

Am I missing something?
Because B lies on x + y = 1, you can write its coordinates as (x, 1 - x).

You know the distance AC, which you have worked out correctly.

You know the distance BC is the same as this. Write an equation for the distance BC using the above version of the coordinates of B, and see there that gets you.
3. (Original post by Pangol)
Because B lies on x + y = 1, you can write its coordinates as (x, 1 - x).

You know the distance AC, which you have worked out correctly.

You know the distance BC is the same as this. Write an equation for the distance BC using the above version of the coordinates of B, and see there that gets you.
So
CB^2 = ((4-(1-x))^2 + (9-x)^2
CB^2 = (x+3)^2 + (9-x)^2
CB^2= 2x^2-12x+90

Then there would I go from here? Would I make the quadratic equal to 122 and solve?

Thanks
4. (Original post by danielwinstanley)
So
CB^2 = ((4-(1-x))^2 + (9-x)^2
CB^2 = (x+3)^2 + (9-x)^2
CB^2= 2x^2-12x+90

Then there would I go from here? Would I make the quadratic equal to 122 and solve?

Thanks
Yes!
5. (Original post by Pangol)
Yes!
Thanks so much

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 15, 2017
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams