Why do you think it matters where the center of dilation is? explain your reasoning.

- A dilation is a type of transformation in which a images is produced with same shape but the different size of any figure.  

For dilation there are two factors which matter in it :-

1. center of dilation - It is the only fixed point or invariant point in a plane which doesn't change with dilation. All the points of dilation will expand or contract about center.It can be located inside, outside or on the figure.

2. scale factor(k≠1) - It tells the ratio of size of dilation to the figure.

when k>1 then its enlargement in size of image

when 0<k<1,then its reduction in size of image

when k=1, then it is congruent image .

it's

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.