Question

part 1 of 4 use the graph at the right. find the vertices of the image of qrtw for a dilation with center (0,0) and a scale factor of 9. a. (simplify your answer. type an ordered pair.)

Explanation:

To solve the problem of finding the vertices of the image of \( QRTW \) after a dilation with center \( (0,0) \) and scale factor \( 9 \), we first need to identify the coordinates of the original vertices \( Q, R, T, W \) from the graph.

Step 1: Identify Original Coordinates

From the graph:

• \( Q \): Let's assume the coordinates of \( Q \) are \( (4, 4) \) (based on the grid).
• \( R \): Let's assume the coordinates of \( R \) are \( (0, 1) \) (based on the grid).
• \( T \): Let's assume the coordinates of \( T \) are \( (3, -3) \) (based on the grid).
• \( W \): Let's assume the coordinates of \( W \) are \( (4, -3) \) (based on the grid).

Step 2: Apply Dilation

A dilation with center \( (0,0) \) and scale factor \( k \) transforms a point \( (x, y) \) to \( (kx, ky) \).

For \( Q(4, 4) \):

\( x' = 9 \times 4 = 36 \)
\( y' = 9 \times 4 = 36 \)
So, \( Q' = (36, 36) \)

For \( R(0, 1) \):

\( x' = 9 \times 0 = 0 \)
\( y' = 9 \times 1 = 9 \)
So, \( R' = (0, 9) \)

For \( T(3, -3) \):

\( x' = 9 \times 3 = 27 \)
\( y' = 9 \times (-3) = -27 \)
So, \( T' = (27, -27) \)

For \( W(4, -3) \):

\( x' = 9 \times 4 = 36 \)
\( y' = 9 \times (-3) = -27 \)
So, \( W' = (36, -27) \)

Final Answer

The vertices of the image \( Q'R'T'W' \) are:

• \( Q' = \boxed{(36, 36)} \)
• \( R' = \boxed{(0, 9)} \)
• \( T' = \boxed{(27, -27)} \)
• \( W' = \boxed{(36, -27)} \)

(Note: The exact coordinates of the original vertices depend on the precise grid in the graph. The above coordinates are based on the assumed grid positions. If the original coordinates are different, the dilated coordinates will change accordingly.)

Answer:

To solve the problem of finding the vertices of the image of \( QRTW \) after a dilation with center \( (0,0) \) and scale factor \( 9 \), we first need to identify the coordinates of the original vertices \( Q, R, T, W \) from the graph.

Step 1: Identify Original Coordinates

From the graph:

• \( Q \): Let's assume the coordinates of \( Q \) are \( (4, 4) \) (based on the grid).
• \( R \): Let's assume the coordinates of \( R \) are \( (0, 1) \) (based on the grid).
• \( T \): Let's assume the coordinates of \( T \) are \( (3, -3) \) (based on the grid).
• \( W \): Let's assume the coordinates of \( W \) are \( (4, -3) \) (based on the grid).

Step 2: Apply Dilation

A dilation with center \( (0,0) \) and scale factor \( k \) transforms a point \( (x, y) \) to \( (kx, ky) \).

For \( Q(4, 4) \):

\( x' = 9 \times 4 = 36 \)
\( y' = 9 \times 4 = 36 \)
So, \( Q' = (36, 36) \)

For \( R(0, 1) \):

\( x' = 9 \times 0 = 0 \)
\( y' = 9 \times 1 = 9 \)
So, \( R' = (0, 9) \)

For \( T(3, -3) \):

\( x' = 9 \times 3 = 27 \)
\( y' = 9 \times (-3) = -27 \)
So, \( T' = (27, -27) \)

For \( W(4, -3) \):

\( x' = 9 \times 4 = 36 \)
\( y' = 9 \times (-3) = -27 \)
So, \( W' = (36, -27) \)

Final Answer

The vertices of the image \( Q'R'T'W' \) are:

• \( Q' = \boxed{(36, 36)} \)
• \( R' = \boxed{(0, 9)} \)
• \( T' = \boxed{(27, -27)} \)
• \( W' = \boxed{(36, -27)} \)

(Note: The exact coordinates of the original vertices depend on the precise grid in the graph. The above coordinates are based on the assumed grid positions. If the original coordinates are different, the dilated coordinates will change accordingly.)