Question

Triangle ABC" is formed using the translation (x+2y+0) and the dilation by a scale factor of

A"BTN
AB -
AB
A"B"
AB
= 2
from the origin. Which equation explains the relationship between AB and A"B"?

Answer 1

The equation explaining the relationship between AB and A'B' is A"B" = [2ABx+4], [2ABy], [1].

Step-by-step explanation:

The translation and dilation can be represented as a single transformation matrix.

The translation matrix is:
[1 0 2]
[0 1 0]
[0 0 1]

The dilation matrix with a scale factor of 2 is:
[2 0 0]
[0 2 0]
[0 0 1]

To find the relationship between AB and A"B", we need to multiply the coordinates of AB by these matrices:

A"B" = Dilation x Translation x AB

Substituting the values in:
A"B" = [2 0 0] x [1 0 2] x [ABx ABy 1]

The resulting equation is:
A"B" = [2ABx+4]
[2ABy]
[1]