The problem states that the given figure is dilated by a factor of $\frac{4}{3}$ centered at the origin. To help you plot the resulting image, let’s work through the dilation process step by step:

Steps to Dilate the Figure:

1. Identify the coordinates of the vertices of the original triangle. From the image, the points seem to be approximately:

   • $Q = (-6, 4)$
   • $P = (6, 4)$
   • $N = (-6, -8)$

2. Apply the dilation formula:

   • Dilation about the origin by a factor of $\frac{4}{3}$ means multiplying each coordinate of the points by $\frac{4}{3}$.

   So, for each vertex $(x, y)$, the new coordinates will be: $(x', y') = \left( \frac{4}{3}x, \frac{4}{3}y \right)$

   • For $Q = (-6, 4)$: $Q' = \left( \frac{4}{3} \times -6, \frac{4}{3} \times 4 \right) = (-8, \frac{16}{3}) \approx (-8, 5.33)$

   • For $P = (6, 4)$: $P' = \left( \frac{4}{3} \times 6, \frac{4}{3} \times 4 \right) = (8, \frac{16}{3}) \approx (8, 5.33)$

   • For $N = (-6, -8)$: $N' = \left( \frac{4}{3} \times -6, \frac{4}{3} \times -8 \right) = (-8, -\frac{32}{3}) \approx (-8, -10.67)$

The dilated coordinates:

• $Q' = (-8, 5.33)$
• $P' = (8, 5.33)$
• $N' = (-8, -10.67)$

These are the new positions of the vertices after dilation. You can now plot these points and connect them to form the dilated image.

Would you like more details or help with plotting this?

Here are 5 follow-up questions:

1. What happens to the angles of a shape after dilation?
2. How does a dilation factor greater than 1 affect the size of the shape?
3. What would the dilation look like with a factor less than 1?
4. Can a dilation move the figure to another quadrant?
5. How do you find the center of dilation if it's not the origin?

Tip: When dilating by a factor $k$, if $k > 1$, the figure enlarges; if $0 < k < 1$, the figure shrinks.