Answer:
3.
Dilation is a transformation that produces an image that is of same shape as the original, but in a different size.
*The value of scale factor ( i.,e k) determines whether the dilation is an enlargement or a reduction.
If
, then the dilation is an enlargement.
If
, then the dilation is a reduction.
To find the scale factor:
In other words, a dilation is a rule that moves points in the plane a specific distance, determined by the scale factor k, from a center O.
Labelled the Blue triangle as A',B', and C'
Also, for black triangle as A, B, and C as you can see the figure shown below in the attachment.
Scale factor is given by;
k =
where O is the origin.
From the figure, A =(1, 2.5) and A' = (2,5)
By distance formula we can find the value of OA' and OA i.e,

Then,

or

Simplify:
k =
>1
therefore, by definition of scale factor, the dilation is an enlargement.
4.
Given: the center of dilation at origin (0,0) with scale factor (c) = 3.
The vertices of ABCD are;
A = (3,0)
B = (1, -2)
C = (3 , -5) and
D = (7 , -1)
The rule of dilation with center of dilation is given by:
where c is the scale factor i.e, c =3
Or we can write it as;
The images of vertices of ABCD are;
= A'(9,0)
=B'(3,-6)
= C'(9,-15)
= D'(21, -3)