Answer this question, 27 points and brainliest!

the coordinates of the center of rotation is (4 , 3)

Step-by-step explanation:

*The line which passes through points (4 , 1) and (4 , 5) is vertical because the points have same x coordinates and its length is 5 - 1 = 4

*The line which passes through points (2 , 3) and (6 , 3) is horizontal because the points have same y coordinates and its length is 6 - 2 = 4

*These two lines intersect each other at their mid-point and this mid-point is the center of rotation

*The mid point is

 or

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: