**answer asap will give brainliest** **pictures shown below** 3. the blue triangle (the larger one) is a dilation image of the black triangle (the smaller one) with the center at the origin. is the dilation an enlargement of a reduction? find the scale factor of the dilation. 4. find the image of the vertices for a dilation with center (0,0) and a scale factor of 3.

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)