Points X and Y are two different points on a circle. Point M is located so that line segment XM and line segment YM have equal length. Which of the following could be true?
I. M is the center of the circle
II. M is on arc XY
III. M is outside of the circle
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
2007-11-07 09:10:00 · 17 answers · asked by Nicole S 2 in Science & Mathematics ➔ Mathematics
All could be true.
If it is the center, then the length from center to circle is always the same.
You can put x and y anywhere on the circle and place M in the middle on the arch and then that is true.
You can put x and y on opposite sides of the circle and then place m at a 90 degree angle to the line xy at the midpoint and it doesn't have to be on the circle.
2007-11-07 09:16:13 · answer #1 · answered by brett s 2 · 0⤊ 0⤋
To find which of A,B C,D,E could be true lets look at the three choices given above.
According to the fact that then M being equidistant from X and Y choice I could be true i.e. If M is the center of the cirlce the XM and YM will be the radi and equal lenght so I could be true.
Since M is located so that XM and YM are equal lengths shows that M could be a point on the arc XY such that it is in the middle of the arc XY and that does not violate choice II and so it could be true.
If M is outside the cirlcle then it could still be equidistant from the points X and Y and so choice III could also be true.
Since choices I & II & III could all be possibly true ( not simulataneously though) so E is the best answer.
2007-11-08 05:34:32 · answer #2 · answered by bunny rabbit 2 · 0⤊ 0⤋
If X and Y are equal distances from M, then M can be anywhere on a line which bisects the line XY in a perpendicular manner. Since the perpendicular bisector of such a line forms part of the method for finding the centre of a circle, the centre is available as a potential location for point M.
This bisecting line will also travel across the circumference of the circle twice (at points diametrically opposed to each other), and so an appearance of point M on the arc XY is also possible.
The line also travels beyond the realms of the circle - thus allowing point M to do the same. Consequently, all three potential locations for point M are valid; the correct answer is therefore 'E'.
I hope this helps, but please feel free to drop me a line if you'd like to go over this or any aspect of mathematical logic further.
2007-11-10 12:42:50 · answer #3 · answered by general_ego 3 · 0⤊ 0⤋
E. XM and YM could be radii, M could be the midpoint of arc XY, or M could just be a random point outside of the circle the same distance from X and Y.
2007-11-07 17:16:39 · answer #4 · answered by shaan 4 · 0⤊ 0⤋
A definately
It can't be II because M cud be on the arc closer to X or Y so XM and YM wud not hav equal lenght.
It can't be III either cus M cud be anywhere oustide the circle!
2007-11-07 17:19:31 · answer #5 · answered by the dude 2 · 0⤊ 1⤋
E
if M is on the outside of the circle, x and Y could still be spaced evenly apart on the circle and the segments could still be equal...
and if it is either I or II, it is possible...
2007-11-07 17:15:25 · answer #6 · answered by sayamiam 6 · 0⤊ 0⤋
if you take the midpoint of a line connecting xy and draw a line from the center of tyhe circle through that midpoint , any point on that line is equal distances from x and y
so answer E is right .
2007-11-07 17:20:38 · answer #7 · answered by mark 6 · 0⤊ 0⤋
It is E as all of the positions that M could possibly be in all fit the answers.
2007-11-07 17:26:17 · answer #8 · answered by Anonymous · 0⤊ 0⤋
E
all 3 are possible
2007-11-07 17:17:43 · answer #9 · answered by Any day 6 · 0⤊ 0⤋
B. But if you get it wrong it's not my fault.
PS Forget it - I ALWAYS get mixed up between segments and sectors.
2007-11-07 17:19:11 · answer #10 · answered by migdalski 7 · 0⤊ 1⤋