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# coordinate geometry help. watch

1. Hello there.

I am having some problems with 11b) of the following question.

The vertex A of a square ABCD is at the point (6,-4). The diagonal BD has equation 2y-x=6, and the vertex B is nearer to the origin than D.(Not sure of the significance of whats in bold)

a)Calculate the coordinates of the centre of the square. I got this to be: (2,4)

b) calculate the coordinates of B and C.

I am not sure how to go about b! Anyideas?
thanks
2. Useful Fact #1: The center of a square is the midpoint of opposite vertices.
3. (Original post by aznkid66)
You should be able to reason that the center of a square is the midpoint of opposite vertices.
yea, but for part B?
4. A and C are opposite vertices. It follows: you know A and the midpoint of AC; thus, you can find C.

Also, if you pay attention to ∆x and ∆y from A to the midpoint with respect to ∆x and ∆y from the midpoint to C, you will probably be able to figure out how to find B.
5. (Original post by aznkid66)
A and C are opposite vertices. It follows: you know A and the midpoint of AC; thus, you can find C.

Also, if you pay attention to ∆x and ∆y from A to the midpoint with respect to ∆x and ∆y from the midpoint to C, you will probably be able to figure out how to find B.
okay I got C, but I am still not sure about coordinates c
6. I assume you mean the coordinates of B?

Hm, I'm not too familiar with C1 and so I'm not sure how you learned this, so maybe you should wait for someone else to help.

But here goes anyway:

Let O be the center of the circle (2,4).
Let ∆x be the change in x coordinates from A to O.
Similarly, let ∆y be the change in y coordinates from A to O.

Knowing that AO is perpendicular to OB, that distance OA is equal to distance OB, and the general direction of O towards B:
What is the change in x coordinates from O to B in terms of ∆x or ∆y?
What is the change in y coordinates from O to B in terms of ∆x or ∆y?

If you understood that, then note that you can also use this method to find point C.

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