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

Reply 1

tonyiptony

First off, draw a picture.

Well, what do you know about right angles (i.e. two lines are perpendicular) in a coordinate system?

Reply 2

Skybird

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.

Reply 3

tonyiptony

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.

Reply 4

Skybird

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.