Question

graph the image of the triangle below using a scale factor of k = 4. write the numerical answer (ie if you get 2 for your answer, type \2\ not \two\)

Explanation:

To solve the problem of graphing the triangle with a scale factor \( k = 4 \), we first need to identify the coordinates of the original triangle's vertices. Let's assume the original vertices are \( S \), \( R \), and \( T \) with coordinates (for example, from the grid):

Step 1: Identify Original Coordinates

Suppose the original coordinates are:

• \( S(1, 0) \)
• \( R(2, 0) \)
• \( T(2, 2) \)

Step 2: Apply Scale Factor

To scale a point \((x, y)\) by a scale factor \( k \), we use the transformation \((x', y') = (k \cdot x, k \cdot y)\).

For \( S(1, 0) \):
\( x' = 4 \cdot 1 = 4 \), \( y' = 4 \cdot 0 = 0 \) → \( S'(4, 0) \)

For \( R(2, 0) \):
\( x' = 4 \cdot 2 = 8 \), \( y' = 4 \cdot 0 = 0 \) → \( R'(8, 0) \)

For \( T(2, 2) \):
\( x' = 4 \cdot 2 = 8 \), \( y' = 4 \cdot 2 = 8 \) → \( T'(8, 8) \)

Step 3: Graph the New Triangle

Plot the points \( S'(4, 0) \), \( R'(8, 0) \), and \( T'(8, 8) \) on the grid and connect them to form the scaled triangle.

(Note: If the original coordinates were different, adjust the calculations accordingly. For example, if the original base was 1 unit and height was 2 units, the scaled base would be \( 1 \times 4 = 4 \) and height \( 2 \times 4 = 8 \), leading to the same result as above.)

Since the problem asks for a numerical answer (possibly the length of a side or a coordinate), let's assume the original base length was 1 (from \( x = 1 \) to \( x = 2 \)) and height was 2 (from \( y = 0 \) to \( y = 2 \)). The scaled base length would be \( 1 \times 4 = 4 \) and scaled height \( 2 \times 4 = 8 \). If the question is about the length of the base or height, the answer would be 4 (base) or 8 (height).

Assuming the question is about the length of the base after scaling:

Answer:

4 (or 8, depending on the specific side; adjust based on original triangle dimensions)