The problem involves a geometric transformation called dilation. Figure $ABCDE$ is being dilated by a scale factor of 3, with the origin $(0,0)$ as the center of dilation, to produce the image $A'B'C'D'E'$.

Key Concepts:

• Dilation: When a figure is enlarged or reduced from a point (the center of dilation), with a scale factor determining how much larger or smaller the figure becomes.
• Scale Factor: In this case, it is 3, meaning the distance of each point from the origin will triple.
• Center of Dilation: The origin $(0, 0)$.

Coordinates of Points:

We need to find the coordinates of point $B'$, which is the transformed version of point $B$.

1. Coordinate of Point $B$:

   • From the graph, the coordinates of point $B$ are $(3, 4)$.

2. Dilation Calculation:

   • Since the scale factor is 3, multiply both coordinates of point $B$ by 3.
   • Coordinates of $B'$: $B'(3 \times 3, 4 \times 3) = B'(9, 12)$

Thus, the ordered pair for the coordinate of $B'$ is $(9, 12)$.

Would you like more details or clarification on the dilation process?

Further Questions:

1. What would be the coordinates of $C'$ after the dilation?
2. How does a dilation affect the angles of a figure?
3. What would happen to the figure if the scale factor was less than 1?
4. How do you determine the center of dilation from a transformation?
5. Can dilation be considered a rigid transformation? Why or why not?

Tip:

When performing a dilation, always multiply both the x- and y-coordinates of each point by the scale factor, keeping the center of dilation constant.