https://file.aiquickdraw.com/mathbot/file/1726706720687epc2q2eq.jpg

In this problem, you're asked to graph the image of a triangle using a scale factor of \( k = 4 \). Here's how we approach it step by step:

1. **Original Coordinates of the Triangle**: 
   The points of the original triangle appear to be \( R(0, 0) \), \( T(1, 2) \), and \( S(2, 1) \).

2. **Scale Factor**: 
   The scale factor is \( k = 4 \), meaning you multiply each coordinate of the triangle by 4.

3. **Calculate the New Coordinates**:
   - For point \( R(0, 0) \): Scaling by 4 gives \( R'(0 \times 4, 0 \times 4) = R'(0, 0) \).
   - For point \( T(1, 2) \): Scaling by 4 gives \( T'(1 \times 4, 2 \times 4) = T'(4, 8) \).
   - For point \( S(2, 1) \): Scaling by 4 gives \( S'(2 \times 4, 1 \times 4) = S'(8, 4) \).

4. **Graph the Image**: 
   Plot the new points \( R'(0, 0) \), \( T'(4, 8) \), and \( S'(8, 4) \) on the grid, then connect them to form the scaled-up triangle.

Would you like any more details or further explanation?

### Related Questions:
1. How do you determine the area of a triangle after scaling?
2. What happens to the perimeter of a shape after scaling by a factor \( k \)?
3. How does the scale factor affect the angles of a shape?
4. Can a shape be reduced instead of enlarged by using a scale factor?
5. What is the difference between enlarging a shape and translating a shape on the coordinate plane?

### Tip:
When scaling, always multiply both the x- and y-coordinates by the same factor to maintain the proportions of the shape.

Graph the image of the triangle using a scale factor of k = 4. The original triangle has vertices at R(0, 0), T(1, 2), and S(2, 1).

Learn how to graph the image of a triangle with vertices R(0, 0), T(1, 2), and S(2, 1) after scaling it by a factor of 4. Understand key concepts of transformation geometry and scaling, including how to calculate new coordinates after applying a scale factor.

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