# AQA A-Level Year 1 Coordinates question

Hello,

Given A( 2, 1) , B( b, 3 ), C( 5, 5 ), b > 3 and angle <ABC = 90 degrees

How do I calculate the value of b ?

TIA

Skybird
First off, draw a picture.

Well, what do you know about right angles (i.e. two lines are perpendicular) in a coordinate system?
Original post by tonyiptony
First off, draw a picture.
Well, what do you know about right angles (i.e. two lines are perpendicular) in a coordinate system?

The first thing that comes to mind is that the gradient of one line is the reciprocal of the other.
Original post by Skybird
The first thing that comes to mind is that the gradient of one line is the reciprocal of the other.

Almost. You missed a minus sign (or really, I like to remember that multiplying two gradients will be -1). But anyhow, a good start.

You now know there is something to do with gradients of two lines (which two in this instance?), then surely it's not a bad idea to just calculate gradients.
As AC is opposite the right-angle we know it is the hypotenuse. If we calculate the gradients of AB and BC we know that the product of the gradients is -1. So after some cross-multiplying, you get to a quadratic which can be factorised giving two values for b: 1 and 6. The question asks for a value of b > 3, so the answer is 6.