Answer:
-2
Step-by-step explanation:
Please note that image ABC in the question has not been dilated about the origin.
The scale factor of the dilated image is -2 as:
- the sides of A'B'C are twice those of ABC.
- A'B'C is on the other side of the given center of dilation (0, 0).
- A'B'C is upside down.
When dilating about a point, the distances from the center of dilation to each vertex are multiplied by the scale factor (see attachment).
When dilating about the origin, we simply multiply the x and y values of the vertices of the pre-image by the scale factor. Therefore, the dilation of image ABC by scale factor -2 is:
Pre-image:
- A = (3, 2)
- B = (1, 3)
- C = (1, 4)
Dilated image:
A' = (3 × -2, 2 × -2) = (-6, -4)
B' = (1 × -2, 3 × -2) = (-2, -6)
C' = (1 × -2, 4 × -2) = (-2, -8)
