Question

Which statements are true for the dilation of triangle DEF according to the rule D_o:(x,y)→(1/2x,1/2y) to create similar triangle D'E'F'?

A. Point F corresponds to F'.
B. Segment EE' is parallel to segment FF.
C. The distance from point D' to the origin is √2/2
​​ times the distance of point D to the origin.
D. The measure of angle E' is the measure of angle E.
E. Triangle ADEF is similar to triangle AD'E'F'.
F. The measure of angle F' is half the measure of angle F.

Answer 1

In the dilation of triangle DEF to create similar triangle D'E'F', points correspond (A is true), and the measure of angles in similar triangles remain the same (D is true, F is false). The distance from the origin to a dilated point is scaled according to the dilation factor (C is true).

Step-by-step explanation:

You asked which statements are true for the dilation of triangle DEF using the rule D_o:(x,y)\u2192(1/2x,1/2y) to create similar triangle D'E'F'.

A. Point F corresponds to F' is true. When a figure is dilated, each point on the original figure has a corresponding point on the dilated figure.

B. Segment EE' is parallel to segment FF isn't explicitly true and cannot be determined without additional information, so we cannot assume this without context.

C. The distance from point D' to the origin is \u221A2/2 times the distance of point D to the origin is true. The dilation factor of 1/2 will reduce the distance from D to the origin by half.

D. The measure of angle E' is the measure of angle E is true. In similar triangles, corresponding angles are congruent.

E. There is no Triangle ADEF to make a comparison, so this statement is not relevant to your question.

F. The measure of angle F' is half the measure of angle F is false. Again, in similar triangles, corresponding angles are congruent, which means they have the same measure, not half.