tricky therom i think its impossibleee ... HELP pleasee?

Question

http://i40.photobucket.com/albums/e215/xxs3xp1stolxx/Picture21.png

Answer 1

Drop a line from P down to the x-axis. This will split the parallel line (in red) so it has two parts. By the definition of midpoint, the x coordinate of the left end is exactly half (the average of the difference) of the x-coordinates (point 0,0 and point P). Similarly the right half will be half the length of its segment. Adding the two parts, the sum of the two halves will be half the length of the bottom side.

The same logic can be used to prove it is parallel because for every point on the line segment RS, it will be halfway between the y coordinate of point O and the y-axis. Since every point is equidistant from the x-axis, the line segment RS must be parallel.

Answer 2

First find the coordinates of R and S, using the midpoint formula.
R = ( (b+0)/2, (c+0)/2) = (b/2, c/2)
S = ( (b+a)/2, (c+0)/2) = ( (b+a)/2, c/2)

To prove it's parallel you need to find its slope and OQ's slope and show they are the same.
Slope QO = (0-0) / (a-0) = 0/a = 0
Slope RS = (c/2 - c/2) / ( (b+a)/2 - b/2) = 0/(a/2) = 0

So they are parallel.

To prove it's half its length use distance formula;

Distance OQ squared = (a-0)^2 + (0-0)^2 = a^2;
square root is a
Distance RS squared = ( (b+a)/2 - b/2)^2 + (c/2 - c/2)^2)

= a/2 squared; sq rt is a/2, so it's half