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15%
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Points X, Y, and Z are located on the rectangular coordinate plane at points (2; 3), (-4; 3), and (2; -3), respectively. What is the length of line segment YZ?
A. 6
B. 6*root(2)
C. 7
D. 8
E. 9
My Q is why cant we use the distance formula for Y / Z and get the length = 6
A. 6
B. 6*root(2)
C. 7
D. 8
E. 9
The OA = B 6*root(2)
My Q is why cant we use the distance formula for Y / Z and get the length = 6
14 Feb 2012, 06:22
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Well of course you can use the distance formula but do realize that the distance formula is not really covered by the Original Guide. Hence, they had to provide a 3rd coordinate to make it a right angled triangle so that you could use the pythagorus theorem. Using the distance formula:
For 2 points: A & B, Distance between A and B \(=\sqrt{({(x_1-x_2)}^2 + {(y_1-y_2)}^2)}\)
Where \(A=(x_1,y_1)\) & \(B=(x_2,y_2)\)
In the question above \(Y=(-4,3)\) & \(Z=(2,-3)\)
Distance between 2 points, Y & Z, on the coordinate system \(=\sqrt{({(-4-2)}^2 + {(3+3)}^2)}\)
Which is \(=\sqrt{(6^2 + 6^2)}\)
Which is \(=\sqrt{72}\)
Which is \(=6\sqrt{2}\)
So Yes, to answer your question, info about \(Y\) & \(Z\) alone is sufficient "if you know the formula for deriving the distance between two coordinates", but otherwise you need to know a third point to first establish it is a right angled triangle. Works either ways. I have seen numerous statistics questions where GMAT actually gives you the formula for calculating the sum of the series, even though we need to know it to solve quite a few question on the GMAT. Either ways, your pick. Answer still remains the same \(=6\sqrt{2}\) and not \(6\)!
For 2 points: A & B, Distance between A and B \(=\sqrt{({(x_1-x_2)}^2 + {(y_1-y_2)}^2)}\)
Where \(A=(x_1,y_1)\) & \(B=(x_2,y_2)\)
In the question above \(Y=(-4,3)\) & \(Z=(2,-3)\)
Distance between 2 points, Y & Z, on the coordinate system \(=\sqrt{({(-4-2)}^2 + {(3+3)}^2)}\)
Which is \(=\sqrt{(6^2 + 6^2)}\)
Which is \(=\sqrt{72}\)
Which is \(=6\sqrt{2}\)
So Yes, to answer your question, info about \(Y\) & \(Z\) alone is sufficient "if you know the formula for deriving the distance between two coordinates", but otherwise you need to know a third point to first establish it is a right angled triangle. Works either ways. I have seen numerous statistics questions where GMAT actually gives you the formula for calculating the sum of the series, even though we need to know it to solve quite a few question on the GMAT. Either ways, your pick. Answer still remains the same \(=6\sqrt{2}\) and not \(6\)!
14 Feb 2012, 06:58
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rxs0005
You can use the distance formula to calculate the length of line segment YZ
The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).
Thus \(YZ=\sqrt{(-4-2)^2+(3-(-3))^2}=6\sqrt{2}\).
Answer: B.
If you are not aware of this formula then you can easily get the answer by drawing the triangle:
Attachment:
xy-plane.PNG [ 15.5 KiB | Viewed 6604 times ]
Answer: B.
For more on Coordinate Geometry check: math-coordinate-geometry-87652.html
Hope it helps.
