The scale factor of the dilation from ABCD to A′B′C′D′ is 3.
Step-by-step explanation:
Step 1:
In the pre-image ABCD, the length of one of the sides is given as 14 units.
For the other shape A′B′C′D′, the same side as the previous shape is given as 8 units.
Step 2:
To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling.
In this case, it is the given length of the sides CD and C′D′.
So the scale factor = [tex]\frac{C^{1} D^{1} }{CD} = \frac{8}{14} = \frac{4}{7} .[/tex]
So the shape ABCD is dilated by a scale factor of [tex]\frac{4}{7}[/tex] to produce the shape A′B′C′D′.
