Question

Figure A'B'C'D' is a dilation of ABCD. What was the scale factor? write a rule for the dilation. (ill send the photo in text it was to big to put here)

Answer 1

Answer:

The scale factor is;

$a=3$

The rule of the dilation is;

$(x,y)\rightarrow(3x,3y)$

Explanation:

The rule of dilation can be writtent in the form;

$(x,y)\rightarrow(ax,ay)$

Where a is the scale factor.

To determine the dilation rule of the given graph, we have to calculate the scale factor of the dilation.

we can do this by dividing the coordinates of the image by that of the preimage;

Let us write the coordinates of D and D';

$\begin{gathered} D=(-2,2) \\ D^{\prime}=(-6,6) \end{gathered}$

The scale factor wil then be;

$\begin{gathered} a=\frac{D^{\prime}}{D}=\frac{-6}{-2} \\ a=3 \end{gathered}$

Since the scale factor a = 3, The rule of the dilation will thenbe;

$\begin{gathered} (x,y)\rightarrow(ax,ay) \\ (x,y)\rightarrow(3x,3y) \end{gathered}$

Therefore, the rule of the dilation is;

$(x,y)\rightarrow(3x,3y)$