Short Answer 
The process of dilation involves identifying the vertices of both the preimage triangle (△ABC) and the image triangle (△A′B′C′), determining that the dilation factor is less than 1, and calculating the scale factor to be 0.75, indicating that the image triangle is a reduced version of the preimage triangle.
Step 1: Identify the Vertices of the Triangles
First, you need to specify the coordinates of the vertices for both the preimage and the image triangles. The preimage triangle ‚ñ≥ABC has vertices defined as:
- A(‚àí5, ‚àí4)
- B(‚àí7, 3)
- C(3, ‚àí2)
The image triangle △A′B′C′ has vertices represented as:
- A′(−3.75, −3)
- B′(−5.25, 2.25)
- C′(2.25, −1.5)
Step 2: Establish the Dilation Factor
Next, determine the dilation factor, which shows how the size relationship between the preimage and image triangle. Since it is given that the size of the preimage is greater than that of the image, we can say:
- 0 < Dilation Factor < 1
This indicates the image is a reduced version of the preimage triangle, leading us to analyze corresponding sides for scale comparisons.
Step 3: Calculate the Scale Factor
Finally, compute the scale factor of the dilation using the lengths of corresponding sides of the triangles. For instance, if the side lengths of triangle △ABC and △A′B′C′ are denoted, you would compare them:
- AB / A′B′ = (Calculated side length of AB) / (Calculated side length of A′B′)
By performing this calculation, the scale factor is found to be:
- 4 / 3 = 0.75
This number confirms the relationship in size between the preimage and the image triangles.