Question
Jeremy wants to verify that the transformation shown is a dilation. He finds the lengths of segments QA and AD to be 4 units.
Point Q is the center of dilation. Triangle A B C is dilated to create triangle D E F. The length of Q A is 4 and the length of A D is 4.
To verify that the transformation is a dilation, Jeremy should also check which of the following? Select three options.
QB = One-halfQE
QC = CF
DE = 2AB
AC = One-halfEF
if BC = 2.25, then EF = 2.25
Point Q is the center of dilation. Triangle A B C is dilated to create triangle D E F. The length of Q A is 4 and the length of A D is 4.
To verify that the transformation is a dilation, Jeremy should also check which of the following? Select three options.
QB = One-halfQE
QC = CF
DE = 2AB
AC = One-halfEF
if BC = 2.25, then EF = 2.25
Answers
GPT-4o mini
To verify that the transformation from triangle ABC to triangle DEF is a dilation centered at point Q, Jeremy should check the following properties:
1. **QB = One-half QE**: This option checks if the ratio of the lengths from Q to the vertices is consistent for the corresponding points in the triangles. If QB is indeed half of QE, it indicates that a dilation factor of 1/2 is being used for these segments.
2. **DE = 2AB**: This option checks if the lengths of the sides of triangle DEF are proportional to the lengths of the sides of triangle ABC according to the dilation factor. A dilation factor of 2 means that DE should be twice the length of AB.
3. **QC = CF**: This option verifies if the lengths from the center of dilation to the points are consistent. If QC equals CF, then it implies that the segments are proportional as per the dilation relationship.
Since he is verifying a crucial characteristic of a dilation (that corresponding lengths are proportional based on the dilation factor), these three options would be useful to confirm the transformation is a proper dilation.
So, the three options Jeremy should check are:
- **QB = One-halfQE**
- **DE = 2AB**
- **QC = CF**
(Note: You can substitute other options where it seems plausible depending on the context of dilation.)
1. **QB = One-half QE**: This option checks if the ratio of the lengths from Q to the vertices is consistent for the corresponding points in the triangles. If QB is indeed half of QE, it indicates that a dilation factor of 1/2 is being used for these segments.
2. **DE = 2AB**: This option checks if the lengths of the sides of triangle DEF are proportional to the lengths of the sides of triangle ABC according to the dilation factor. A dilation factor of 2 means that DE should be twice the length of AB.
3. **QC = CF**: This option verifies if the lengths from the center of dilation to the points are consistent. If QC equals CF, then it implies that the segments are proportional as per the dilation relationship.
Since he is verifying a crucial characteristic of a dilation (that corresponding lengths are proportional based on the dilation factor), these three options would be useful to confirm the transformation is a proper dilation.
So, the three options Jeremy should check are:
- **QB = One-halfQE**
- **DE = 2AB**
- **QC = CF**
(Note: You can substitute other options where it seems plausible depending on the context of dilation.)