GMAT Prep: Geometry

erdnah · Posted: Mon Aug 27, 2007 11:04 am Post subject: GMAT Prep: Geometry

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).

radhika1306 · Posted: Mon Aug 27, 2007 11:37 am Post subject:

C
Both statements are needed

erdnah · Posted: Mon Aug 27, 2007 11:58 am Post subject:

can you explain?

Bharat · Posted: Mon Aug 27, 2007 11:32 pm Post subject:

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)

erdnah · Posted: Tue Aug 28, 2007 1:35 am Post subject:

thanks a lot @bharat! Very Happy

Bharat · Posted: Fri Aug 31, 2007 1:21 am Post subject:

You are welcome Erdnah!! Smile