To dilate $\triangle ABC$ by a scale factor of 3, we follow the basic principles of dilation with respect to a center and a given scale factor.

Steps to Dilate $\triangle ABC$:

1. Identify the center of dilation: In this case, the center of dilation is the point $D$, shown in the diagram.
2. Apply the scale factor: The scale factor given is 3, which means that each vertex of the triangle will move three times farther away from point $D$ along the line connecting $D$ to the respective vertex.
3. Determine the new positions of points:
   • Draw a straight line from point $D$ through each vertex of $\triangle ABC$.
   • Measure the distance from $D$ to each vertex and multiply it by 3.
   • Plot the new points for $A'$, $B'$, and $C'$ at three times the distance along the same lines.

The final result will be a new triangle, $\triangle A'B'C'$, which is three times the size of the original triangle, with each corresponding side length being three times as long.

Would you like me to calculate the new coordinates of the dilated triangle based on the grid, or do you have any other questions?

5 Related Questions:

1. What is the formula to dilate a point using a given center and scale factor?
2. How would the coordinates change for different scale factors (e.g., 2, 4, or negative values)?
3. How do you find the center of dilation in a geometric figure?
4. What happens to the angles of a triangle after dilation?
5. How can you apply dilation transformations in real-world scenarios?

Tip: When performing dilation, ensure the distances from the center of dilation to the vertices are consistent with the given scale factor.