Question

What sequence of transformations, when applied to △XYZ , shows that △XYZ is similar to △X′Y′Z′ ?

dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down

dilation with respect to the origin by a scale factor of 12 followed by a translation of 2 units up

translation of 4 units down followed by a dilation with respect to the origin by a scale factor of 12

translation of 4 units down followed by a dilation with respect to the origin by a scale factor of 2

Answer 1

dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down

Explanation:

Answer 2

The coordinates of Δxyz ⇒⇒ x(1,1) y(2,3) z(3,2)
The coordinates of Δx'y'z' ⇒⇒ x'(2,-2) y'(4,2) z'(6,0)

1. Applying the transformation of the first sentence on Δxyz
The results are ⇒⇒⇒ (2,-2) (4,2) (6,0)

2. Applying the transformation of the second sentence on Δxyz
The results are ⇒⇒⇒ (12,14) (24,38) (36,28)

3. Applying the transformation of the third sentence on Δxyz
The results are ⇒⇒⇒ (12,-36) (24,-12) (36,-24)

4. Applying the transformation of the fourth sentence on Δxyz
The results are ⇒⇒⇒ (2,-6) (4,-2) (6,-4)

By comparing the results obtained with the coordinates of Δx'y'z'
So, the correct answer is the first sentence.
dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down