75 points to whoever does all of this for me.

1. draw, in black, the triangle with vertices (-3, 2), (1, 1), and (2, 5).

2. draw the triangle's image under the dilation (x, y ) → (2x, 2y).

3. explain clearly why the two triangles must be similar.

4. how could a dilation create a figure which is congruent to the original one? [hint: there are two ways.]

(share imgur link)

Whenever an image goes under dilation we multiply the co-ordinates of each vertex with a scale factor (k).

Points (x,y) becomes (2x,2y) so the scale factor is 2.

Step-by-step explanation:

1.The diagram is shown below.

2.The co-ordinates (-3,2),(1,1) and (2,5) will become (-6,4),(2,2) and (4,10).

3.Dilated figures are similar.

The two triangles must be similar as we can see = = 2

We can find the length of AC,ZY,BC and XY by using distance formula.

Distance formula  =

                         AC= = Approx 8

                         BC= =Approx 8

For triangle XYZ

                      ZY==Approx 4

                      XY==Approx 4

= = 2

Similar triangles must have proportional side lengths.

Statement:Two figures are said to be similar when one figure can be obtained from the other by a single transformation that includes translation, reflection, rotation and dilation,the size may not be same.

So in above question the triangles are undergoing dilation with a positive scale factor,hence both are similar.

4.Dilation and congruence.

When the scale factor is equivalent to one (1).

The dilation create a figure which is congruent to the original one.

Similarity preserves shape, but not necessarily size making the figures similar.It is possible for similar figures to have a scale factor of 1 then it can be said that all congruent figures are also similar.  

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total