das.ashmita wrote:What is the co-ordinate of A
1. A is 2 units away from (3,4)
2. A is 3 units away from (0,0)
OA: C
DRAW.
ALWAYS LOOK FOR SPECIAL TRIANGLES.
There are an infinite number of points that will satisfy each statement on its own.
Statements 1 and 2 combined:
Triangle OBC is a 3-4-5 triangle.
The distance between point B and the origin is 5.
Since point A must be 3 units from the origin and 2 units from point B -- for a total of 3+2 = 5 units -- point A must be located EXACTLY as shown in the drawing above.
Thus, the coordinates of point A can be determined.
SUFFICIENT.
The correct answer is
C.
We can use SIMILAR triangles to determine point A's x-coordinate.
Triangle OBC is similar to triangle OAD.
Thus, corresponding sides must be in the same ratio:
OB/OA = OC/OD.
Since OB=5, OA=3 and OC=3, we get:
5/3 = 3/OD
OD = 9/5.
Thus, the x-coordinate of point A = 9/5.
Similar reasoning can be used to determine point A's y-coordinate.
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