Question

1. select all of the true statements about the dilation shown below.

the center of dilation is located at (-2, 9).
the scale factor is a number greater than 1.
the scale factor is a number less than 1.
the bigger image is the original shape.
the smaller image is the original shape.

Explanation:

Step1: Analyze Center of Dilation

To find the center of dilation, we check the intersection of lines through corresponding points (e.g., \( L \) and \( L' \), \( M \) and \( M' \), \( N \) and \( N' \)). The lines through these points intersect at a point, not \((-2, 9)\), so the first statement is false.

Step2: Analyze Scale Factor

Compare the size of the original and dilated figures. The bigger figure (with \( L, M, N \)) and the smaller (with \( L', M', N' \)): since the dilated figure (\( L', M', N' \)) is smaller, the scale factor is less than 1 (because a scale factor \( k < 1 \) shrinks the figure). So "scale factor < 1" is true, "scale factor > 1" is false.

Step3: Analyze Original Shape

The bigger image (with \( L, M, N \)) is the original, and the smaller (\( L', M', N' \)) is the dilation. So "The bigger image is the original shape" is true, "The smaller image is the original shape" is false.

Answer:

• The scale factor is a number less than 1.
• The bigger image is the original shape.