Question

A. Describe a dilation (center and scale factor) that transforms triangle RST into triangle R'S'T' or explain why it cannot be done.
b.In either case, use complete sentences to describe the relationship that exists between the corresponding sides and angles

(I'll attach the illustration for the problem below)

Answer 1

To find the center of enlargement, draw a line that connects corresponding vertices, as shown below. 

The transformation that map RST to R'S'T' is an enlargement with scale factor of  3 and center of (0,0)

Answer 2

Answer:  The center of dilation is the origin (0, 0) and scale factor is 3.

Step-by-step explanation:  We are given to describe a dilation that that transforms ΔRST to ΔR'S'T', or to explain why it cannot be done.

We can see in the figure provided that both the triangles are right-angles at angles S and S'

Also, RS = ST = 1 unit   and   R'S' = S'T' = 3 units.

Using Pythagoras theorem, we have

$RT^2=RS^2+ST^2=1^2+1^2=2\\\\\Rightarrow RT=\sqrt 2,$

and

$R'T'^2=R'S'^2+S'T'^2=3^2+3^2=18\\\\\Rightarrow R'T'=3\sqrt 2.$

Therefore, the ratio of the corresponding sides will be

$\dfrac{R'S'}{RS}=\dfrac{3}{1}=3,~~\dfrac{S'T'}{ST}=\dfrac{3}{1}=3,~~~\dfrac{R'T'}{RT}=\dfrac{3\sqrt 2}{\sqrt 2}=3\\\\\\\dfrac{R'S'}{RS}=\dfrac{S'T'}{ST}=\dfrac{R'T'}{RT}=3.$

Since the ratio of the corresponding sides are equal, so the two triangles are similar.

Hence, ΔRST can be dilated to form ΔR'S'T'.

The center of dilation will be origin (0, 0), because the shapes of the two triangles are same with respect to the origin.

Also, since the ratio of any two corresponding sides of the triangles is 3, so the scale factor is 3.

Thus, ΔRST can be dilated to ΔR'S'T' with origin (0, 0) as the center of dilation and scale factor 3.