GMAT Prep: Geometry

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erdnah: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jun 12, 2007 12:57 am

by erdnah » Mon Aug 27, 2007 11:04 am

If a and b are both positive numbers, what are the coordinates of the midpoint of the line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b).
(2) The coordinates of D are (1-a, b).

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Source: Beat The GMAT — Data Sufficiency | Mon Aug 27, 2007 11:04 am

radhika1306: Master | Next Rank: 500 Posts; Posts: 144; Joined: Fri Apr 13, 2007 2:25 am

by radhika1306 » Mon Aug 27, 2007 11:37 am

C
Both statements are needed

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erdnah: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jun 12, 2007 12:57 am

by erdnah » Mon Aug 27, 2007 11:58 am

can you explain?

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Bharat: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Jul 22, 2007 11:43 pm; Thanked: 8 times

by Bharat » Mon Aug 27, 2007 11:32 pm

For obtaining midpoint coordinates of a line segment, you need to take average of x & y coordinates of the endpoints respectively.

Using any one piece of information, you can't solve (because the other end is unknown); however, if you use both the pieces together, the answer is:
x-coordinate = (a + (1-a))/2 = 1/2 [i.e. average of x coordinates of both ends]
y-coordinate = (b + (1-b))/2 = 1/2 [i.e. average of y coordinates of both ends]
=> Midpoint is (1/2, 1/2)

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erdnah: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jun 12, 2007 12:57 am

by erdnah » Tue Aug 28, 2007 1:35 am

thanks a lot @bharat!

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Bharat: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Jul 22, 2007 11:43 pm; Thanked: 8 times

by Bharat » Fri Aug 31, 2007 1:21 am

You are welcome Erdnah!!

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