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To find the co-ordinates of point Q

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To find the co-ordinates of point Q

by gmattesttaker2 » Thu Nov 28, 2013 11:19 am
Hello,

Can you please assist with this:

What are the (x, y) coordinates of point Q if point Q is equidistant from the four
vertices of square ABCD and the (x, y) coordinates of A, B, and D are,
respectively, (2, 1), (2, 4), and (5, 1)?

(A) (2.5, 2)
(B) (2.5, 2.5)
(C) (3.5, 2.5)
(D) (4, 4)
(E) (5, 4)

OA: C

My approach was as follows:

I was thinking that since AC is a diagonal, length of AC = (s)(square root of 2) = 3.sqroot of 2
Hence, AQ = 1.5 x sqroot of 2

Can you please tell me why this would be in-correct?

Thanks,
Sri
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by [email protected] » Thu Nov 28, 2013 1:11 pm
Hi Sri,

Your approach calculated the length of the "half-way" point up the diagonal of the square. That's NOT what the question asked for. If you take a look at your drawing, you'll likely notice the easiest approach to this question. If you want the mid-point of the square, then find the x-co-ordinate that is midway between 2 and 5 and the y-co-ordinate that is midway between 1 and 4.

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by theCodeToGMAT » Thu Nov 28, 2013 8:57 pm
Answer [spoiler]{C}[/spoiler]
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by Mathsbuddy » Fri Nov 29, 2013 9:09 am
We are only interested in horizontal (x) and vertical (y) components:

Horizontal midpoint = (5 + 2)/2 = 3.5
Vertical midpoint = (4 + 1)/2 = 2.5

Answer is (C) (3.5, 2.5)

So no need for any clever diagonal business! :)
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