If rectangle abcd, defined by the coordinates a(0, 0), b(0, -4), c(-2, -4), d(-2, 0), is dilated by a scale factor of 2, with resulting vertex a' at (2, 4), what is the center of the dilation? a) (0, 0) eliminate b) (2, 4) c) (0, -4) d) (-2, -4)

D) (-2, -4).

Step-by-step explanation:

Let be the center of dilation. Imagine that is the center of origin of a new Cartesian Plane. What would the coordinates of point A and A' on the new plane?

Dilating about the "origin" of the new plane by a factor of two will give the point , also on the new plane.

For coordinates of A' on the original plane,

.

As a result,

.

.

.

In other words, is the center of dilation.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft