rewrite this essay
rewrite this essay and make it more simple To prove to Mark that the 8-ball at point I is equidistant from the holes at points F and C, we can use the properties of perpendicular bisectors.
Let's denote the midpoint of FC¯¯¯¯¯¯¯¯ as point M. Since GH¯¯¯¯¯¯¯¯ is the perpendicular bisector of FC¯¯¯¯¯¯¯¯, it divides FC¯¯¯¯¯¯¯¯ into two equal halves. Therefore, IM¯¯¯¯¯¯¯¯ is also the perpendicular bisector of FC¯¯¯¯¯¯¯¯, and point I is equidistant from points F and C.
Since point I lies on the perpendicular bisector IM¯¯¯¯¯¯¯¯, it is equidistant from both F and C. Thus, the 8-ball at point I is equidistant from the holes at points F and C.
This demonstrates that regardless of where Mark strikes the 8-ball along the perpendicular bisector GH¯¯¯¯¯¯¯¯, it will always be equidistant from the holes at points F and C. Therefore, Mark can aim for either hole with the same probability of sinking the 8-ball.
1 answer
Because point I is on the perpendicular bisector IM, it is equidistant from both F and C. Therefore, the 8-ball at point I is the same distance from the holes at points F and C.
This proves that no matter where Mark hits the 8-ball along the line GH, it will always be equidistant from the holes at points F and C. Mark can aim for either hole with an equal chance of sinking the 8-ball.