To solve this problem, let's go through the dilation process.

Problem Breakdown:

• Original Figure: ABCD
• Scale Factor: 2
• Center of Dilation: (0, 0)

Steps to Dilate the Figure:

1. Identify the coordinates of the original vertices of quadrilateral ABCD.

   • Let's denote the vertices as $A(x_1, y_1)$, $B(x_2, y_2)$, $C(x_3, y_3)$, and $D(x_4, y_4)$.
   • From the image:
     • $A(-3, 1)$
     • $B(-1, 3)$
     • $C(1, 3)$
     • $D(3, 1)$

2. Apply the scale factor of 2 to each vertex, using the formula: $(x', y') = (k \cdot x, k \cdot y)$ where $k$ is the scale factor (which is 2 in this case).

   So, the new coordinates will be:

   • $A'(-6, 2)$
   • $B'(-2, 6)$
   • $C'(2, 6)$
   • $D'(6, 2)$

3. Plot the new coordinates $A', B', C', D'$ on the graph to form the dilated quadrilateral.

Would you like to proceed with additional details on this process or have any specific questions about it?

Relative Questions:

1. What is the general formula for dilating a point with respect to a different center of dilation?
2. How would the shape change if the scale factor was less than 1?
3. What happens to the area of the quadrilateral after dilation with a scale factor of 2?
4. How would the coordinates change if the dilation were centered at a different point, say (1,1)?
5. Can you identify any properties of the quadrilateral that remain unchanged after dilation?

Tip:

Always double-check the new coordinates after applying the scale factor to ensure accuracy in geometric transformations.