Answer:
Scale Factor ≈ 0.67
P'Q' Length = 10
Step-by-step explanation:
To find the scale factor, a relationship must be found between the original points, and the dilated points. To do this, simply divide the new points by the old points.
P to P' : \(\frac{2}{3}=0.6667\) AND \(\frac{4}{6}=0.6667\)
Q to Q' : \(\frac{8}{12}=0.6667\) AND \(\frac{12}{18}=0.6667\)
Therefore, the scale factor is 0.6667 ≈ 0.67
The length of P'Q' can be calculated with the distance formula:
\(d^{2}=(y_{1}-y_{2} )^{2} +(x_{1}-x_{2} )^{2} \\d^{2} =(4-12)^{2} + (2-8)^{2} \\d^{2} =(-8)^{2} +(-6)^{2} \\d^{2} =64+36\\d=\sqrt{100} =10\)
Alternatively, you could multiply the length of PQ with the scale factor to find P'Q':
15*0.6667=10
