Question
Segment Segment X Y is dilated through point M with a scale factor of 2. Which segment shows the correct result of the dilation?
Point M is the center of dilation. Segment A E has length of 1.5, B F has a length of 2, X Y has a length of 3, C G has a length of 5, and D H has a length of 6.
AE
BF
CG
DH
Point M is the center of dilation. Segment A E has length of 1.5, B F has a length of 2, X Y has a length of 3, C G has a length of 5, and D H has a length of 6.
AE
BF
CG
DH
Answers
GPT-4o mini
To find the result of the dilation of segment XY through point M with a scale factor of 2, we need to multiply the length of segment XY by the scale factor. The length of segment XY is given as 3.
After applying the scale factor:
\[ \text{New length} = \text{Original length} \times \text{Scale factor} \]
\[ \text{New length} = 3 \times 2 = 6 \]
Now, we need to identify which of the segments A E, B F, C G, and D H has a length of 6. The lengths of the segments are:
- Segment AE: 1.5
- Segment BF: 2
- Segment CG: 5
- Segment DH: 6
The segment that shows the correct result of the dilation (length of 6) is **Segment DH**.
After applying the scale factor:
\[ \text{New length} = \text{Original length} \times \text{Scale factor} \]
\[ \text{New length} = 3 \times 2 = 6 \]
Now, we need to identify which of the segments A E, B F, C G, and D H has a length of 6. The lengths of the segments are:
- Segment AE: 1.5
- Segment BF: 2
- Segment CG: 5
- Segment DH: 6
The segment that shows the correct result of the dilation (length of 6) is **Segment DH**.