Question

The sequence that maps shape i onto shape ii is a reflection across the x-axis, and then a dilation by a scale factor of ____.

a) 0.5
b) 1
c) 2
d) -1

Answer 1

After reflecting a shape across the x-axis, the dilation scale factor to map shape i onto shape ii, when the object size changes from 2.0 cm to 5.0 cm, is 2.5.

Step-by-step explanation:

The sequence that maps shape i onto shape ii is a reflection across the x-axis, followed by a dilation. To determine the scale factor of the dilation, we need to compare the size of the original shape with the size of the final shape. If an image of a 2.0-cm object reflected from a mirror is 5.0 cm tall, the magnification is the ratio of the image size to the object size, which is 5.0 cm / 2.0 cm = 2.5. Therefore, the scale factor of dilation after the reflection must be 2.5, aligning with option b).