Find the equation of the perpendicular bisector between a(-3,5) and a'(3,5)

a bisector of a line, is simply one line that cuts it into two equal halves.

we know the line is a bisector, for the segment A(-3,5) and A'(3,5), now, we could use the midpoint formula to get the midpoint, but there's no need, notice, the y-coordinate is the same for both, y = 5, meaning is just a horizontal line

so the line must pass through 0,5.

now, we could find the slope AA', and since it's a horizontal line, we'd get a 0

and get the negative reciprocal of that, for the slope of the perpendicular and so forth.  However, there's no need, a perpendicular line to a horizontal line, is just a vertical line, so is really a vertical line passing through (0,5), so is right on the smack at the y-axis.

x = 0.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.