Question

http://imgur.com/MVkRn

"What happens to P as a -> 0" (see image above)
M is in the middle of the line segment AO.

The answer is 1/2 but I can't figure out how.

Answer 1

use midpt formula to get coordinates of point M
use rise/run slope formula to get slope of line O-M-A
use perpendicular to get slope of line M-P
find the coordinates of P = the intercept of the line M-P (from its slope and point M) in terms of "a"
notice that the y-coordinate is 1/2 when a->0