Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

$s(\square,\square)$

$t(\square,\square)$

$u(\square,\square)$

$v(\square,\square)$

Explanation:

Step1: Determine the original coordinates

From the graph, the original coordinates are \( S(0,0) \), \( T(0,2) \), \( U(2,2) \), \( V(2,0) \).

Step2: Apply the dilation formula

The formula for dilation centered at the origin with scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here \( k = 5 \).

• For \( S(0,0) \): \( S'(5\times0,5\times0)=(0,0) \)
• For \( T(0,2) \): \( T'(5\times0,5\times2)=(0,10) \)
• For \( U(2,2) \): \( U'(5\times2,5\times2)=(10,10) \)
• For \( V(2,0) \): \( V'(5\times2,5\times0)=(10,0) \)

Answer:

\( S'(0,0) \), \( T'(0,10) \), \( U'(10,10) \), \( V'(10,0) \)