Source: OG (11ed) p25 #36 (Diagnostic)
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?
1) The length of the line segment XY is 3
2) The length of the line segment OY is 1.5
Answer: B (#2 is sufficient)
My Answer: E - while X and Y are on the same plane, you are not told if circle C exists on that same plane. You can easily imagine two planes intersecting where the point X on plane 1 is contained in the circle on plane 2 while point Y is not. The key here is that they introduced the idea of three dimensional plotting with the use of 'planes'. For the answer they propose you must assume that the circle and the points are on the same plane - which is not clear in the question. (If you are having a hard time visualizing this, see https://en.wikipedia.org/wiki/Image:Plan ... ection.png)
I suspect that I am simply over thinking the problem as I have a background in mathematics and have to work in three space from time to time. Is it a safe assumption that 3 space cartesian questions won't be found on the test and this question is just poorly written?
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?
1) The length of the line segment XY is 3
2) The length of the line segment OY is 1.5
Answer: B (#2 is sufficient)
My Answer: E - while X and Y are on the same plane, you are not told if circle C exists on that same plane. You can easily imagine two planes intersecting where the point X on plane 1 is contained in the circle on plane 2 while point Y is not. The key here is that they introduced the idea of three dimensional plotting with the use of 'planes'. For the answer they propose you must assume that the circle and the points are on the same plane - which is not clear in the question. (If you are having a hard time visualizing this, see https://en.wikipedia.org/wiki/Image:Plan ... ection.png)
I suspect that I am simply over thinking the problem as I have a background in mathematics and have to work in three space from time to time. Is it a safe assumption that 3 space cartesian questions won't be found on the test and this question is just poorly written?
This test really does just go up to high-school level Algebra 2. Seriously advanced math that might address various things differently just doesn't get tested here. So, yes, don't worry about it!
