Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).  
It has to be in the format of the picture below.

Answer 1

We are given that

a line is perpendicular bisector on line between point (4,1) and (2,-5)

So, line intersect at mid-point between (4,1) and (2,-5)

so, firstly we will find mid-point

$(a,b)=(\frac{4+2}{2},\frac{1-5}{2})$

$(a,b)=(3,-2)$

now, we will find slope between (4,1) and (2,-5)

x1=4 , y1=1

x2=2 , y2=-5

slope is

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{-5-1}{2-4}$

$m=3$

now, our required line is perpendicular to this line

so, slope of required line is -1/m

so, we get slope

$m'=\frac{-1}{3}$

we have a point as (3 ,-2)

we can use point slope form of line

$y-y_1=m'(x-x_1)$

we can plug values

$y+2=-\frac{1}{3}(x-3)$

now, we can solve for y

$y=-\frac{1}{3}x-1$................Answer