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Argand diagram FP2

http://filestore.aqa.org.uk/subjects/AQA-MFP2-W-MS-JUN15.PDF

Question 5

How does one accomplish part b?

You can construct a Cartesian equation for L because you know that the line perpendicular to it goes through the point 2-4i thus (2,-4) as well as the origin. You can work out the gradient of L by taking the negative reciprocal of the gradient from O to 2-4i. Once you have the equation, just see where the line intersects the axis and that should give you the points A and B. The mid point will be half of these co-ordinates along their respective axis (real and imaginary).

For the second part, it states the circle goes through A and B, therefore the centre is the mid-point between the two points. You know it goes though O so just take the magnitude of C for the radius of the circle.

(edited 7 years ago)

Reply 2

IrrationalRoot

Original post by RDKGames

For the second part, it states the circle goes through A and B, therefore the centre is the mid-point between the two points.

I don't think this is sufficient. You assume that A and B are diametrically opposite with no explanation. It must be mentioned that they are diametrically opposite since

\angle AOB

is a right angle.

Reply 3

RDKGames

Study Forum Helper

Original post by IrrationalRoot

I don't think this is sufficient. You assume that A and B are diametrically opposite with no explanation. It must be mentioned that they are diametrically opposite since

\angle AOB

is a right angle.

It's 2 marks and they accept it without that explanation, but to be fair I was never really good at circle theorems to begin with so that's probably for the best :biggrin:

Reply 4

IrrationalRoot

Original post by RDKGames

It's 2 marks and they accept it without that explanation, but to be fair I was never really good at circle theorems to begin with so that's probably for the best :biggrin:

Yeah you're right they don't require the explanation although they really should.

Dw I'm not great with circle theorems either (Still haven't tried proving them to this day! Really should soon.), recently I spent over an hour on a STEP Q unable to do it simply because I didn't remember a certain circle theorem lol.