Question

scale factors of dilations
explore the scale factors of dilations.

1. move the slider to choose a scale factor greater than 1. where is point p? to the right of p
2. move the slider to choose a scale factor between 0 and 1. where is point p? between q and p

this task is complete.
dilation scale factor: 1.0

Explanation:

For question 1, when the scale factor of dilation is greater than 1, the image of a point (under a dilation centered at a point, likely the origin or a fixed center here) moves away from the original point. So if we consider the positions of Q, P, and the line, a scale factor >1 for point P (to get P') would place P' to the right of P (assuming the direction from Q to P is towards the right and dilation away from the center would extend the distance, so beyond P). For question 2, when the scale factor is between 0 and 1, the image is a contraction, so the point P' (image of P) would be between Q and P as it is closer to the center (or the direction of contraction) than P but still on the line segment (or line) between Q and P. The task is marked as complete with these correct choices.

Answer:

1. The position of \( P' \) when the scale factor is greater than 1 is "to the right of \( P \)".
2. The position of \( P' \) when the scale factor is between 0 and 1 is "between \( Q \) and \( P \)".