Question
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answers
Answered by
GPT-4o mini
When performing a dilation, the lengths from the center of dilation to the vertices of the original triangle are multiplied by the scale factor. In this case, the scale factor is 4 (from the notation \( DO,4 \)).
Since you are given that the length of line segment \( OB \) is \( \frac{3}{4} \), you can find the length of line segment \( OB' \) as follows:
\[
OB' = \text{Scale factor} \times OB
\]
Substituting the scale factor and the length of \( OB \):
\[
OB' = 4 \times \frac{3}{4}
\]
Calculating this gives:
\[
OB' = 3 \text{ units}
\]
Thus, the length of \( OB' \) is **3 units**.
Since you are given that the length of line segment \( OB \) is \( \frac{3}{4} \), you can find the length of line segment \( OB' \) as follows:
\[
OB' = \text{Scale factor} \times OB
\]
Substituting the scale factor and the length of \( OB \):
\[
OB' = 4 \times \frac{3}{4}
\]
Calculating this gives:
\[
OB' = 3 \text{ units}
\]
Thus, the length of \( OB' \) is **3 units**.