Question

15 points!!!

Two right triangles are shown below.
Which statement is true?
There is a dilation centered at the origin with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at (-2,0) with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at a point off of the x-axis transforming triangle I into triangle III.
There is no dilation transforming triangle I into triangle III.

Answer 1

There is no dilation transforming triangle I into triangle II.

Explanation:

Answer 2

The correct option is 4.

Explanation:

If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.

In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.

In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.

`(1)/(1)\\eq (1)/(2)`

The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.

Therefore the correct option is 4.