Question

a axel started to dilate figure abcd using (0, 0) as the center of dilation. he graphed point b. what scale factor did he use? b complete the dilation to create figure abcd.

Explanation:

Step1: Identify coordinates of B and B'

Let's assume the coordinates of point B are $(3,0)$ and the coordinates of point B' are $(6,0)$ (by observing the grid).

Step2: Calculate scale - factor formula

The formula for the scale - factor $k$ of a dilation with center at the origin $(0,0)$ is $k=\frac{x_{B'}}{x_{B}}$ (when considering the x - coordinates, and it's the same for y - coordinates if they are non - zero). Here, $x_{B} = 3$ and $x_{B'}=6$.

Step3: Calculate the scale - factor

$k=\frac{6}{3}=2$

Step4: Complete the dilation for other points

To find the coordinates of A', C', and D', we multiply the coordinates of A, C, and D by the scale - factor 2.
If the coordinates of A are $(- 2,3)$, then the coordinates of A' are $(-2\times2,3\times2)=(-4,6)$.
If the coordinates of C are $(1,-1)$, then the coordinates of C' are $(1\times2,-1\times2)=(2,-2)$.
If the coordinates of D are $(-2,-2)$, then the coordinates of D' are $(-2\times2,-2\times2)=(-4,-4)$. Then we can plot these points to form figure A'B'C'D'.

Answer:

a. The scale factor is 2.
b. Plot points A'(-4,6), B'(6,0), C'(2,-2), D'(-4,-4) to form figure A'B'C'D'.