On a map, the distance between two cities is 5.6 inches. If the map uses a scale of 2 inches represents 20 miles, what is the actual distance between the two cities in miles?

Answer:

A" (-3, 0)

B" (9, 9)

C" (9, 0)

Step-by-step explanation:

The hint explains how to get the final coordinates.

The original figure ABC has vertices

A (-3, -1)
B (1, 2)

C (1, -1)

There are two separate transformations for this triangle, so let's take it one step at a time

The first transformation is a translation by the vector <2, 1>, This means we get a new figure A'B'C' where we add 2 to each of the x coordinates of the original figure and 1 to the y coordinates of the original figure

For A which is (-3,-1) the transformed coordinate becomes:
A -> A' -> A' (-3 + 2, -1 + 1) => A'(-1, 0)

Similarly

B(1, 2) -> B' is B'(1 + 2, 2 + 1) => B'(3, 3)

C(1, -1) -> C'(1 + 2, -1 + 1) or C'(3, 0)

So the first transformation results in a triangle A'B'C' with the following coordinates:

A'(-1, 0)
B'(3, 3)
C'(3, 0)

The second transformation is a dilation of A'B'C' which results in an expansion or compression of the image depending on the scale factor. Here the scale factor is 3 so the image is expanded by a factor of 3

Dilation simply requires you to multiply both x and y coordinates oof A'B'C' by 3

A' (-2 , 0) -> A"(-1 x 3, 0 x 3) => A"(-3, 0)
B'(3, 3) -> B"(9, 9)
C'(3, 0) -> C"(9, 0)

I have attached two images showing each of the transformations separately to give you a better idea