Question

1. find the order pairs after a dilation scale factor 2 center of dilation the origin. graph the image. scale factor = 2 p : __________ , q : ________ r : ________ , s : __________

Explanation:

Step1: Identify original coordinates

From the graph, we determine the original coordinates:

• \( P(-3, -2) \)
• \( Q(2, -2) \)
• \( R(4, 1) \)
• \( S(-1, 1) \)

Step2: Apply dilation rule

The rule for dilation with scale factor \( k \) centered at the origin is \( (x, y) \to (kx, ky) \). Here, \( k = 2 \).

For \( P' \):

Multiply \( P \)'s coordinates by 2:
\( P(-3, -2) \to P'(2 \times -3, 2 \times -2) = (-6, -4) \)

For \( Q' \):

Multiply \( Q \)'s coordinates by 2:
\( Q(2, -2) \to Q'(2 \times 2, 2 \times -2) = (4, -4) \)

For \( R' \):

Multiply \( R \)'s coordinates by 2:
\( R(4, 1) \to R'(2 \times 4, 2 \times 1) = (8, 2) \)

For \( S' \):

Multiply \( S \)'s coordinates by 2:
\( S(-1, 1) \to S'(2 \times -1, 2 \times 1) = (-2, 2) \)

Answer:

\( P'(-6, -4) \), \( Q'(4, -4) \)
\( R'(8, 2) \), \( S'(-2, 2) \)