A level Maths help

An engineer is making a circular disc.
A model of the disc is drawn as a circle on a set of axes such that it passes
through coordinate points P (–1, –1), Q (5, k) and R(7, 3)
Given that angle PRQ is 90°, find the value of k and the area of the disc

I can’t figure out how to do this I drew a diagram and I don’t see a right angle could someone please show me how to do it

An engineer is making a circular disc.
A model of the disc is drawn as a circle on a set of axes such that it passes
through coordinate points P (–1, –1), Q (5, k) and R(7, 3)
Given that angle PRQ is 90°, find the value of k and the area of the disc

I can’t figure out how to do this I drew a diagram and I don’t see a right angle could someone please show me how to do it

Anything about semicircles and right angles ring any bells?

are you sure it is PRQ that is a right angle??

Nope I’m a first year so haven’t done anything in a while the only thing I managed to come up with is (5,7) but that’s where I get confused about where the circle is on the graph I assumed that r was the midpoint and p was on the circumference but that would mean that (5,7) would just be along the diameter.

An engineer is making a circular disc.
A model of the disc is drawn as a circle on a set of axes such that it passes
through coordinate points P (–1, –1), Q (5, k) and R(7, 3)
Given that angle PRQ is 90°, find the value of k and the area of the disc

I can’t figure out how to do this I drew a diagram and I don’t see a right angle could someone please show me how to do it

Agree with (5,7) as the position of Q. All of P,Q,R are on the circumference.

Since PRQ is a right angle, it follows that PQ is a diameter. Hence work out radius and area.

Thanks for your help I got confused with where the circle was but now l understand

Thanks but I don’t think that q can be (5,10.75) because it wouldn’t be on the line perpendicular (y=-2x+17) to PR (y=0.5x+0.5) thus making PRQ not 90°

yeah i guess that would make my answer wrong then, I can't think of another way to do it but I might have made a numerical or simplifying error somewhere so you could always retry it and be more careful than me and see if it gets an answer that works lol

Thanks but I don’t think that q can be (5,10.75) because it wouldn’t be on the line perpendicular (y=-2x+17) to PR (y=0.5x+0.5) thus making PRQ not 90°

actually you could try a method of simultaneous equations of the lines PR and QR to solve for K

I am uploading a link to my worked solution, this is how I would've done it, sorry the sketch is not the best. https://imgur.com/crl9ZeI

Hi i know this was a year ago but i was doing the question and i read through your method which seemed correct but on the markscheme it puts k=7 and the area=25 x pi

An engineer is making a circular disc.
A model of the disc is drawn as a circle on a set of axes such that it passes
through coordinate points P (–1, –1), Q (5, k) and R(7, 3)
Given that angle PRQ is 90°, find the value of k and the area of the disc

I can’t figure out how to do this I drew a diagram and I don’t see a right angle could someone please show me how to do it

Hey, for any of those still struggling;