Answer:
(a) Scale factor: [tex]k = \frac{2}{3}[/tex]
(b) See attachment
Step-by-step explanation:
Given
See attachment for ABCD and QRST
Solving (a): The scale factor of ABCD to QRST
This is calculated as:
[tex]k * ABCD = QRST[/tex]
Considering corresponding sides AB and QR
[tex]AB = 42cm;\ QR = 28cm[/tex]
[tex]k * AB = QR[/tex]
[tex]k * 42 = 28[/tex]
Make k the subject
[tex]k = \frac{28}{42}[/tex]
[tex]k = \frac{2}{3}[/tex]
Solving (b): Reproduce ABCD at scale factor of [tex]\frac{1}{2}[/tex]
The new rectangle will have the following side lengths.
[tex]AB' = \frac{1}{2} * AB[/tex]
[tex]AB' = \frac{1}{2} * 42[/tex]
[tex]AB' = 21[/tex]
[tex]BC' = \frac{1}{2} * BC[/tex]
[tex]BC' = \frac{1}{2} * 21[/tex]
[tex]BC' = 10.5[/tex]
