Final answer:
A dilation that produces a congruent figure has a scale factor of 1. For the scale drawing of a swimming pool with a scale factor of 1/72 and a diameter of 1.5 inches, the actual diameter of the swimming pool is calculated to be 9 feet.
The correct answer is B.
Step-by-step explanation:
If a dilation produces a congruent figure, then the scale factor was equal to 1. A dilation that results in a congruent figure does not change the size of the figure, meaning its proportions and dimensions remain the same. Therefore, the only scale factor that would produce a figure identical to the original is 1.
Now, let's look at the scale drawing of a swimming pool. The diameter of the pool in the scale drawing is 1(1/2) inches, and the scale factor is 1/72. To find the actual diameter, we use the ratio:
scale/actual = 1/72
Since we know the scale measurement,
1(1/2) inches = 1.5 inches, we set up the proportion:
1.5 inches / actual diameter in feet = 1/72
To solve for the actual diameter, we multiply both sides by the actual diameter and then divide both sides by 1/72 to isolate the actual diameter:
actual diameter = 1.5 inches * 72
Since there are 12 inches in a foot, we convert 1.5 inches to feet by dividing by 12:
actual diameter in feet = (1.5 * 72) / 12
actual diameter in feet = 108 / 12
actual diameter in feet = 9
Therefore, the actual diameter of the swimming pool is 9 feet.