Question

1. graph the image of the triangle below using a scale factor of ( k = 4 ).
2. graph the image of the rectangle below using a scale factor of ( k = 5/2 ).
3. graph the image of the quadrilateral below using a scale factor of ( k = 1/3 ).
4. graph the image of the triangle below using a scale factor of ( k = 3/4 ).
5. identify the scale factor used to graph the image below.
6. identify the scale factor used to graph the image below.

Explanation:

To solve these problems, we'll focus on problem 7 as an example (the process is similar for others). Let's assume the coordinates of the original triangle's vertices (from the grid):

Step 1: Identify Original Coordinates

Looking at the triangle with vertices \( S \), \( T \), \( U \):

• Let’s assume \( S = (1, 1) \), \( U = (2, 1) \), \( T = (2, 2) \) (adjust based on grid; these are estimates for illustration).

Step 2: Apply Scale Factor \( k = 4 \)

To scale a point \( (x, y) \) by \( k \), multiply \( x \) and \( y \) by \( k \):

• For \( S(1, 1) \): \( S' = (1 \times 4, 1 \times 4) = (4, 4) \)
• For \( U(2, 1) \): \( U' = (2 \times 4, 1 \times 4) = (8, 4) \)
• For \( T(2, 2) \): \( T' = (2 \times 4, 2 \times 4) = (8, 8) \)

General Process for All Problems:

1. Find Original Coordinates: Locate each vertex on the grid (count horizontal/vertical units from axes).
2. Apply Scale Factor: Multiply each coordinate (\( x \) and \( y \)) by \( k \) to get the image’s coordinates.
3. Graph the Image: Plot the new coordinates and connect them.

For example, for problem 7 (triangle with \( k = 4 \)):

• If \( S = (1, 1) \), \( U = (2, 1) \), \( T = (2, 2) \) (adjust if grid differs), then:
• \( S' = (4, 4) \)
• \( U' = (8, 4) \)
• \( T' = (8, 8) \)

For Identifying Scale Factor (Problems 11, 12):

1. Find Corresponding Points: Locate a vertex and its image.
2. Calculate Ratio: Divide the image’s coordinate by the original’s (e.g., if \( G = (1, 1) \) and \( G' = (3, 3) \), scale factor \( k = 3/1 = 3 \)).

Final Answer (for Problem 7, example):

\( S'(4, 4) \), \( U'(8, 4) \), \( T'(8, 8) \) (adjust based on actual grid coordinates).

(Repeat this process for other problems by identifying original coordinates, applying \( k \), and graphing.)

Answer:

To solve these problems, we'll focus on problem 7 as an example (the process is similar for others). Let's assume the coordinates of the original triangle's vertices (from the grid):

Step 1: Identify Original Coordinates

Looking at the triangle with vertices \( S \), \( T \), \( U \):

• Let’s assume \( S = (1, 1) \), \( U = (2, 1) \), \( T = (2, 2) \) (adjust based on grid; these are estimates for illustration).

Step 2: Apply Scale Factor \( k = 4 \)

To scale a point \( (x, y) \) by \( k \), multiply \( x \) and \( y \) by \( k \):

• For \( S(1, 1) \): \( S' = (1 \times 4, 1 \times 4) = (4, 4) \)
• For \( U(2, 1) \): \( U' = (2 \times 4, 1 \times 4) = (8, 4) \)
• For \( T(2, 2) \): \( T' = (2 \times 4, 2 \times 4) = (8, 8) \)

General Process for All Problems:

1. Find Original Coordinates: Locate each vertex on the grid (count horizontal/vertical units from axes).
2. Apply Scale Factor: Multiply each coordinate (\( x \) and \( y \)) by \( k \) to get the image’s coordinates.
3. Graph the Image: Plot the new coordinates and connect them.

For example, for problem 7 (triangle with \( k = 4 \)):

• If \( S = (1, 1) \), \( U = (2, 1) \), \( T = (2, 2) \) (adjust if grid differs), then:
• \( S' = (4, 4) \)
• \( U' = (8, 4) \)
• \( T' = (8, 8) \)

For Identifying Scale Factor (Problems 11, 12):

1. Find Corresponding Points: Locate a vertex and its image.
2. Calculate Ratio: Divide the image’s coordinate by the original’s (e.g., if \( G = (1, 1) \) and \( G' = (3, 3) \), scale factor \( k = 3/1 = 3 \)).

Final Answer (for Problem 7, example):

\( S'(4, 4) \), \( U'(8, 4) \), \( T'(8, 8) \) (adjust based on actual grid coordinates).

(Repeat this process for other problems by identifying original coordinates, applying \( k \), and graphing.)