To solve this problem, we will first analyze the information provided. The problem describes a triangle $\triangle ABC$, with vertices $A(6, 4)$, $B(10, 12)$, and $C(6, 2)$, which is enlarged to another triangle $\triangle A_1B_1C_1$ with vertices $A_1(6, 4)$, $B_1(10, 12)$, and $C_1(12, 14)$.

Steps to Approach:

1. Understanding the enlargement:

   • The vertices $A$ and $A_1$, and $B$ and $B_1$ are identical, which means the enlargement is centered in such a way that these points don't move. However, the vertex $C$ has moved to $C_1$, so this gives us the clue that the scaling only affected certain portions of the triangle.

2. Draw Triangle ABC:

   • Plot the points $A(6, 4)$, $B(10, 12)$, and $C(6, 2)$ on a coordinate plane.
   • Connect the points to form the triangle.

3. Draw Triangle A1B1C1:

   • Plot the points $A_1(6, 4)$, $B_1(10, 12)$, and $C_1(12, 14)$ on the same coordinate plane.
   • Connect the points to form the enlarged triangle.

Would you like me to provide a visualization of these two triangles on a coordinate plane?

5 related questions:

1. What is the scale factor of the enlargement for the triangle?
2. How can we find the center of enlargement based on the given points?
3. What are the properties of enlargements in coordinate geometry?
4. How does the movement of point C affect the shape of the triangle?
5. What are the formulas for finding distances between points in a triangle?

Tip: When dealing with enlargements, always check if any of the points remain stationary, as this can help locate the center of enlargement.