Coordinates

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Nov 16, 2011 2:19 pm

On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle's diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?

A. (3, 3/2)
B. (1, 2/2)
C. (0, -4)
D. (2/2, 1)
E. (-1, -2/2)

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Source: Beat The GMAT — Problem Solving | Wed Nov 16, 2011 2:19 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Nov 16, 2011 3:02 pm

Let y = mx + c be the equation of the diameter.
Point (2,1) is a point on the line. so, 1 = 2m + c - (1)
Point (4,6) is a point on the line. so, 6 = 4m + c - (2)
From (1) and (2) m = 5/2 ; c = -4

Equation of the line y = (2.5)x - 4 and point B lies on the equation. Point(0,-4) satisfies the equation. Option C

Anil Gandham
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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Nov 16, 2011 7:15 pm

MBA.Aspirant wrote:On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle's diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?

A. (3, 3/2)
B. (1, 2/2)
C. (0, -4)
D. (2/2, 1)
E. (-1, -2/2)

Solution:
Use the midpoint formula.
(2, 1) is the midpoint of (x, y) and (4, 6).
So, (x+4)/2 = 2 and (y+6)/2 = 1
Or x = 0 and y = -4
Or A is (0, -4).

The correct answer is C.

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ariz: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Tue May 17, 2011 8:51 pm; Thanked: 9 times

by ariz » Thu Nov 17, 2011 12:40 pm

MBA.Aspirant wrote: A. (3, 3/2)
B. (1, 2/2)
C. (0, -4)
D. (2/2, 1)
E. (-1, -2/2)

Are you sure these answer choices are correct? These just came out to be either 1 or -1...

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