Answer:
we conclude that:
- If the scale factor > 1, the image is stretched
- If the scale factor < 1, the image is reduced
- If the scale factor = 1, the image and object will be congruent
Step-by-step explanation:
A dilation is a transformation which generates an image that is the same shape as the original object but in a different size.
The image can be obtained by multiplying the measure of the original object by a scale factor.
If the scale factor > 1, the image is stretched
If the scale factor < 1, the image is reduced
If the scale factor = 1, the image and object will be congruent
For example, if we multiply the measure of the coordinates of the vertex A(2, 2) of a triangle by a scale factor of 2, the image A' is stretched as the scale factor > 1.
Dilation with scale factor 2, multiply by 2.
A(2, 2) → (2(2), 2(2)) = A'(4, 4)
So, the image point A'(4, 4) is enlarged.
Dilation with scale factor ½, multiply by ½.
A(2, 2) → (2(1/2), 2(1/2)) = A'(1, 1)
So, the image point A'(1, 1) is reduced.
Therefore, we conclude that:
- If the scale factor > 1, the image is stretched
- If the scale factor < 1, the image is reduced
- If the scale factor = 1, the image and object will be congruent
