Determine whether one figure is a dilation of the other. Complete the justification. Quadrilateral DEFG has side lengths of 20 m, 24 m, 28 m, and 16 m. Quadrilateral D'E'F'G' has side lengths of 45 m, 54 m, 63 m, and 36 m.

The figure D'E'F'G' (is/not) a dilation of the figure DEFG. The ratios of the lengths of the corresponding sides (are/are not) equal.

Step-by-step explanation:

We can figure the ratios of corresponding sides as ...

  45/20 = 2.25

  54/24 = 2.25

  63/28 = 2.25

  36/16 = 2.25

The ratios of corresponding sides are equal, so the figures are dilations of each other.

Additional comment

Another way to look at corresponding sides is to find the ratio each side has to the other sides in the same figure.

  20 : 24 : 28 : 16 = 5 : 6 : 7 : 4 . . . . . . multiples of 4

  45 : 54 : 63 : 36 = 5 : 6 : 7 : 4 . . . . . . multiples of 9

The reduced ratios are the same, so corresponding sides are proportional. (The ratio of larger to smaller is 9/4 = 2.25.)

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: