Question

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

Answer 1

Answer:

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

Step-by-step 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 = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Side AB is along x-axis, side AB =

$\sqrt{(2-0)^2+(2-2)^2}\\\Rightarrow \sqrt{4}\\\Rightarrow 2\ units$

Similarly side, BC = 2 units

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

$\sqrt{(1+4)^2+(-1- (-1))^2}\\\Rightarrow \sqrt{25}\\\Rightarrow 5\ units$

B'C' = 5 units

The ratio of sides:

AB : A'B' = 2:5

$\Rightarrow \dfrac{AB}{A'B'} = \dfrac{2}{5}\\\Rightarrow A'B' = \dfrac{5}{2} AB$

So, scaling factor is $\dfrac{5}{2}$ or 2.5.

OR

Scaling factor is Five-halves.

Answer 2

Answer:

The answer is C on Edge.

Step-by-step explanation: