The problem asks to "Dilate △ABC by a scale factor of 4, centered at the origin."

In dilation, each point of the triangle will be multiplied by the scale factor, keeping the origin (0, 0) as the center of dilation.

Let's go through the steps for the dilation:

1. Identify the coordinates of points A, B, and C:

Based on the image:

• A ≈ (-2, 2)
• B ≈ (1, 1)
• C ≈ (3, 2)

2. Apply the dilation formula:

The dilation formula is: $(x', y') = (k \cdot x, k \cdot y)$ where $k$ is the scale factor (4 in this case), and $(x, y)$ are the coordinates of each point.

Now, dilate each point:

• For A (-2, 2): $A' = (4 \cdot -2, 4 \cdot 2) = (-8, 8)$
• For B (1, 1): $B' = (4 \cdot 1, 4 \cdot 1) = (4, 4)$
• For C (3, 2): $C' = (4 \cdot 3, 4 \cdot 2) = (12, 8)$

3. Plot the new points A', B', and C':

• A' = (-8, 8)
• B' = (4, 4)
• C' = (12, 8)

These new points form the dilated triangle A'B'C' with a scale factor of 4, keeping the shape similar but scaled up in size.

Let me know if you would like further details or clarifications on this.

Related Questions:

1. What happens if you use a scale factor less than 1?
2. How do you calculate the area of the original and dilated triangles?
3. Can dilation change the angles of the triangle?
4. What would happen if the dilation center was not the origin?
5. How would you apply this to 3D shapes?

Tip:

When applying dilation, always remember that distances between points and the center of dilation are multiplied by the scale factor, but angles remain unchanged.