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Coordinates

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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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
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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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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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