Question
The scale factor of the dilation of segment HG is One-sixth.
Point P is the center of dilation. Line segment H G is dilated to form shorter line segment H prime G prime. The length of P G prime is 0.5
If PG' equals 0.5 units, what is PG?
Point P is the center of dilation. Line segment H G is dilated to form shorter line segment H prime G prime. The length of P G prime is 0.5
If PG' equals 0.5 units, what is PG?
Answers
Answered by
GPT-4o mini
To find the length of \( PG \), we can use the relationship between the lengths in a dilation. Given that the scale factor of the dilation is \( \frac{1}{6} \) (one-sixth), we can express this relationship mathematically.
The formula for the length after dilation is:
\[
PG' = \text{scale factor} \times PG
\]
Substituting the given values, we have:
\[
0.5 = \frac{1}{6} \times PG
\]
To find \( PG \), we can rearrange the equation:
\[
PG = 0.5 \div \frac{1}{6}
\]
Dividing by a fraction is the same as multiplying by its reciprocal, so:
\[
PG = 0.5 \times 6 = 3
\]
Thus, the length of \( PG \) is \( \boxed{3} \) units.
The formula for the length after dilation is:
\[
PG' = \text{scale factor} \times PG
\]
Substituting the given values, we have:
\[
0.5 = \frac{1}{6} \times PG
\]
To find \( PG \), we can rearrange the equation:
\[
PG = 0.5 \div \frac{1}{6}
\]
Dividing by a fraction is the same as multiplying by its reciprocal, so:
\[
PG = 0.5 \times 6 = 3
\]
Thus, the length of \( PG \) is \( \boxed{3} \) units.