The point A has the coodinates (2 , 5)

The point B has the coodinates (6 , 7)

The equation of AB is y = 1/2x + 4

Find the equation of the perpendicular bisector to AB

We need to find the mid-point of AB....this is :

[ (2 + 6)/2, (5 + 7) /2) = ( 8 / 2, 12 / 2) = (4, 6)

The perpendicular bisector will go through this point...and it will have a slope of -2

So .....its equation is

y = -2 ( x - 4) + 6

y = -2x + 8 + 6

y = -2x + 14

Can you explain where the x-4 came from please

The equation is

y = m(x - h) + k

Where m is the slope of the perpendicular bisector.....and ( h, k) = ( 4, 6) which is a point on the perpedicular bisector....in this case, it's the midpoint of AB