Question

dilations

1. multiple choice 2 points

7.
$\frac{pz}{px}=\frac{py}{py}=\frac{px}{pz}$
$\frac{px}{px}=\frac{py}{py}=\frac{pz}{pz}$
$\frac{px}{px}=\frac{pz}{py}=\frac{py}{pz}$
$\frac{py}{px}=\frac{px}{py}=\frac{pz}{pz}$

1. numeric 2 points
2. the scale factor is __. answer

Explanation:

Step1: Recall dilation property

In a dilation, the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the pre - image is equal to the scale factor for all points. So for a dilation with center \(P\), \(\frac{PX'}{PX}=\frac{PY'}{PY}=\frac{PZ'}{PZ}\).

Step2: Calculate scale factor

The scale factor \(k\) of a dilation is given by the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the pre - image. Given \(UE = 2\) cm (distance on pre - image) and \(UE'=10\) cm (distance on image) with center of dilation \(U\), the scale factor \(k=\frac{UE'}{UE}\).
\[k = \frac{10}{2}=5\]

Answer:

1. B. \(\frac{PX'}{PX}=\frac{PY'}{PY}=\frac{PZ'}{PZ}\)
2. 5