Final answer:
In geometry, to dilate a triangle with a scale factor means to proportionally resize it using a center point, and the dilated triangle maintains the same angles as the original triangle. Thus, when Triangle PARK is dilated with a center point C and a scale factor of 3/4, the angles remain unchanged—angle Q' will have the same measure as angle Q.
Step-by-step explanation:
The question 'Dilate Triangle PARK using center C and scale factor 3/4' pertains to the mathematical concept of dilation in geometry. Dilation is a transformation that produces an image with the same shape as the original, but is a different size. The scale factor determines how much larger or smaller the image will be compared to the original figure.
To perform a dilation, each point of the original figure is moved along a line away from or toward a fixed center of dilation (point C), and the distance each point is moved is multiplied by the scale factor. In this case, using a scale factor of 3/4 means that each point of Triangle PARK will be positioned 3/4 of the distance from the center C compared to its original distance.
Regarding the properties of dilations and the angle Q', we know that dilations preserve angles. So, the measure of angle Q' in the dilated triangle will be equal to the measure of angle Q in the original Triangle PARK.