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Midpoint: (1, 1)

Perpendicular slope: 2

Equation of perpendicular bisector: y = 2x-1

Explanation:

The coordinates of the midpoint will be the average coordinate of A and B.

First, let's find the average x coordinate of A and B. That would be (-5+7)/2=1 Now, let's find the average y coordinate of A and B. That would be (2+(-4))/2=1

Therefore, the coordinates of the midpoints are (1, 1).

Now, to find the perpendicular slope, we need to find its slope first, which is (change in y) / (change in x) = (-2-4)/(7-(-5)) = -6/12 = -1/2.

To find the perpendicular slope, you take the negative reciprocal. So in this case, the perpendicular slope would be 2.

Now, to find the equation of the perpendicular bisector, we can set up an equation with a slope of 2:

y=2x

But notice when that equation's x coordinate is 1, its y coordinate is 2, but we want it to be 1. Therefore, we subtract 1 from the right hand side:

y=2x-1

Therefore, the perpendicular bisector will be y=2x-1.