Let's analyze each question in the image:

Question 1:

Statement: If $k = 5$ and the center of dilation is point $O$, then $OA' = 5OA$.

• A dilation with a scale factor $k$ means that the distance from the center of dilation $O$ to a point $A'$ is scaled by $k$ times the distance from $O$ to $A$.
• Since $k = 5$, this means $OA' = 5 \cdot OA$.
• This statement is true.

Question 2:

Statement: What will the image look like after a pre-image has been dilated by a scale factor of 1?

• A scale factor of 1 means that the image retains the same size as the pre-image.
• Thus, the image will neither expand nor shrink.
• The correct answer is: It will be the same size as the pre-image.

Would you like a more detailed explanation of these concepts or have any other questions?

Related Questions:

1. What happens to the size of a shape when the scale factor is greater than 1?
2. How does the position of the center of dilation affect the final image?
3. What is the effect of a negative scale factor in dilation?
4. If the scale factor is $\frac{1}{2}$, what happens to the distances from the center of dilation?
5. How do you determine the coordinates of a point after a dilation?

Tip:

A scale factor of less than 1 shrinks the image, while a scale factor greater than 1 enlarges it.