Question

Triangle A B C with vertices (0, 4), (6, 2), (2, 2), undergoes a sequence of transformations. Jasmine believes it's a dilation of 1/2, a rotation of 180°, and a translation down 5 and left 1. Terrence thinks it's a dilation of 1/2, a reflection over the x-axis, and a translation of 4 left. Who is correct?

a) Jasmine
b) Terrence
c) Both
d) Neither

Answer 1

Without further information on the final appearance or position of the triangle, we cannot determine if Jasmine or Terrence is correct. Both sequences include a dilation of 1/2, but their subsequent steps differ, suggesting that at least one is incorrect.

Step-by-step explanation:

To determine which sequence of transformations correctly describes the changes to triangle ABC with vertices (0, 4), (6, 2), and (2, 2), we should consider each step given by Jasmine and Terrence and apply them to the triangle.

For Jasmine's sequence:

1. A dilation of 1/2 will scale the triangle down in size, keeping the shape proportional.
2. A rotation of 180° will turn the triangle upside down.
3. A translation down 5 and left 1 will move the triangle to a new location.

For Terrence's sequence:

1. Again, a dilation of 1/2 will scale the triangle down in size.
2. A reflection over the x-axis will flip the triangle over the x-axis.
3. A translation of 4 left will move the triangle to the left.

As the problem does not provide information on the final position or size of the triangle, there is not enough information to determine if the sequences are incorrect or correct. Both Jasmine's and Terrence's sequences involve a dilation of 1/2, but their other steps are different, suggesting at least one of them must be incorrect if there is a single correct transformation sequence. However, we cannot definitively say which one (if any) is right without additional information on the resulting position or appearance of the triangle.