Triangle AOB has vertices A(4,4), O(0,0), and B(8,0). EF right bisects AB at P. GH right bisects OA at Q. Determine the coordinates of the circumcentre of triangle DEF.

Question

I really need help, please. Today, my teacher just gave us all this work for over the weekend saying that the book would explain it all, but I've read the chapter a million time and I can't even begin to understand the question.

Answer 1

Your question makes no sense to me.
How long is EF, do we know the endpoints E and F?
You want the circumcentre of triangle DEF, but D is not mentioned in your data.

Please restate correctly.

Answer 2

that's all the question says. I've tried to interpret it different ways, but I just don't know... The back of the book says the answer is (4,0), but there's no more info.

Answer 3

(4,0) would be the correct centre for the circumcentre of the original triangle ABO

in general, the circumcentre is the intersection of any two of the rightbisectors of two of the sides of the original triangle.

The right bisector of a side goes through the midpoint of that side and is perpendicular to it. I think that is why they mentioned P and Q.

e.g. to find the equation of the right bisector of OA first find Q which would be (2,2). The slope of OA is 1 so the slope of the perpendicular is -1, (the negative reciprocal)
The equation of the right bisector is then y = -x + b
sub in (2,2)
2 = -2 + b, ..... b = 4

equation is y = -x + 4

Find the equation of the right bisector of AB in the same way.
Solving, you should find that (4,0) will be the intersection of those two lines

Answer 4

thank you so very much!
You've been so helpful!

Answer 5

Your suppose to use AOB, not DEF since the book make an error.