Question

Triangle ABC was dilated and translated to form similar triangle A'B'C'.

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6).

What is the scale factor of the dilation?

One-fifth
Two-fifths
Five-halves
5

Answer 1

The answer is C on Edge.

Explanation:

Answer 2

Dilation is done by the scale factor of Five-halves.

Explanation:

Please refer to the image attached,

The graph clearly shows the triangles
`\triangle`ABC and
`\triangle`A'B'C'.

Let us calculate the sides of triangles first then we will be able to find scale factor of dilation.

Using the distance formula:

Distance between 2 points
`P (x_1,y_1) \text{ and } Q (x_2,y_2)` is given by formula:

PQ =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Side AB is along x-axis, side AB =

`√((2-0)^2+(2-2)^2)\\\Rightarrow √(4)\\\Rightarrow 2\ units`

Similarly side, BC = 2 units

Now, in
`\triangle`A'B'C', A'B' can be calculated by distance formula:

`√((1+4)^2+(-1- (-1))^2)\\\Rightarrow √(25)\\\Rightarrow 5\ units`

B'C' = 5 units

The ratio of sides:

AB : A'B' = 2:5

`\Rightarrow (AB)/(A'B') = (2)/(5)\\\Rightarrow A'B' = (5)/(2) AB`

So, scaling factor is
`(5)/(2)` or 2.5.

OR

Scaling factor is Five-halves.