Question

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

$q(\square,\square)$

$r(\square,\square)$

$s(\square,\square)$

Explanation:

Step1: Find the original coordinates

From the graph, the coordinates are \( Q(-2,-2) \), \( R(-2,2) \), \( S(2,-2) \).

Step2: Apply the dilation formula

The formula for dilation centered at the origin with scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here \( k = 4 \).
For \( Q(-2,-2) \):
\( Q'=(4\times(-2),4\times(-2))=(-8,-8) \)
For \( R(-2,2) \):
\( R'=(4\times(-2),4\times2)=(-8,8) \)
For \( S(2,-2) \):
\( S'=(4\times2,4\times(-2))=(8,-8) \)

Answer:

\( Q'(-8,-8) \), \( R'(-8,8) \), \( S'(8,-8) \)