Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Find original coordinates

From the graph, the original coordinates are:

• \( S(-2, -1) \)
• \( T(0, -1) \)
• \( U(2, 2) \)
• \( V(-2, 2) \)

Step2: Apply dilation formula

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 4 \).

For \( S(-2, -1) \):
\( x' = 4 \times (-2) = -8 \), \( y' = 4 \times (-1) = -4 \), so \( S'(-8, -4) \)

For \( T(0, -1) \):
\( x' = 4 \times 0 = 0 \), \( y' = 4 \times (-1) = -4 \), so \( T'(0, -4) \)

For \( U(2, 2) \):
\( x' = 4 \times 2 = 8 \), \( y' = 4 \times 2 = 8 \), so \( U'(8, 8) \)

For \( V(-2, 2) \):
\( x' = 4 \times (-2) = -8 \), \( y' = 4 \times 2 = 8 \), so \( V'(-8, 8) \)

Answer:

\( S'(-8, -4) \), \( T'(0, -4) \), \( U'(8, 8) \), \( V'(-8, 8) \)