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01 May 2008, 08:28
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If, on a coordinate plane, point A has the coordinated (-3, 4), how far is point A from point E?
1) Point E is on the y-axis four units from the origin.
2) If point A were twice as far from point E, it would be the same distance from point E as point C is at coordinates (0, -2).
1) Point E is on the y-axis four units from the origin.
2) If point A were twice as far from point E, it would be the same distance from point E as point C is at coordinates (0, -2).
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01 May 2008, 10:03
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The answer is C. First, draw a picture. Then here's my reasoning:
1. Insufficient We know point A has coordinates (-3, 4) and the question states point E is on the y-axis 4 points from the origin, therefore it has the points (0, Y), where Y can be equal to 4 or -4. This would give us two different distances from point A. At (0, -4) and at (0, 4) line segment AE would be two different lengths.
2. Inufficient The question says 2AE = EC, or twice the distance between AE would equal the distance between points E and C. Now it might be helpful to plot both points C and A on a graph to get a visual idea of the problem. One thing not to do here is think you have two sides of a 30-60-90 right triangle, x and 2x because you have no idea where point E is located, expect the distance between A and E is exactly half the distance between E and C.
Now try and combine the statements. Plot each point on the graph. You'll see E must be (0, 4) for this problem to work. And plug in the numbers to the formula in 2.
2 AE = (4 - (-2)) or 2AE = 6, and the distance between points A and E (-3, 4) and (0, 4) = 3, then multiply that by 2 and you get 6.
1. Insufficient We know point A has coordinates (-3, 4) and the question states point E is on the y-axis 4 points from the origin, therefore it has the points (0, Y), where Y can be equal to 4 or -4. This would give us two different distances from point A. At (0, -4) and at (0, 4) line segment AE would be two different lengths.
2. Inufficient The question says 2AE = EC, or twice the distance between AE would equal the distance between points E and C. Now it might be helpful to plot both points C and A on a graph to get a visual idea of the problem. One thing not to do here is think you have two sides of a 30-60-90 right triangle, x and 2x because you have no idea where point E is located, expect the distance between A and E is exactly half the distance between E and C.
Now try and combine the statements. Plot each point on the graph. You'll see E must be (0, 4) for this problem to work. And plug in the numbers to the formula in 2.
2 AE = (4 - (-2)) or 2AE = 6, and the distance between points A and E (-3, 4) and (0, 4) = 3, then multiply that by 2 and you get 6.
03 May 2008, 09:54
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Should be 'B'.
Stmt1: E can be (0,4) or (0,-4).
So AE is not known.
insuff
Stmt2: 2AE = AC
we know co-ordinates of A and C, so AC can be determined, hence the AE
Suff
Stmt1: E can be (0,4) or (0,-4).
So AE is not known.
insuff
Stmt2: 2AE = AC
we know co-ordinates of A and C, so AC can be determined, hence the AE
Suff
