Using the stated facts, the statements from the listed options which are true are given by: Option A) Circle F and circle D are similar.
How to find if a pair of figure is not dilated version of each other?
Dilation of a figure will leave its size get scaled (multiplied) by same number.
Thus, suppose if a circle is dilated with its center as center of dilation, with some scale factor, that will affect its radius.
So, if the current circle is having the radius 'r' units, and the circle is dilated from its center with scale factor of S, then, we get:
New circle's radius = [tex]S \times r \: \rm units[/tex]
For the given case, the three facts to be considered are:
- Circle D has center (2, 3) and radius 7.
- Circle F is a translation of circle D, 2 units right.
- Circle F is a dilation of circle D with a scale factor of 2.
Since circle F is translation of circle D, 2 units right, so its all points will be shifted 2 units right, which makes coordinate (x,y) - > (x + 2, y) (since height is same, only the x coordinates shifted to right side).
Thus, center of F would be (2 + 2, 3) = (4,3).
Since there is scaling of the circle D scale factor 2, thus, radius of circle F will be twice the radius of the circle D, which will be 2 times 7 = 14 units.
Since dilated figures are similar, thus, Circle F and Circle D are similar.
(similar figures are those who look alike, although may be smaller or larger versions, but congruent figures are exact same dimension holding figures, their all properties match, but positions can be different).
Thus, the correct statement is only option A: Circle F and circle D are similar.
Learn more about dilation here:
https://brainly.com/question/3266920
