Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.
t((□, □))
u((□, □))
v((□, □))
w((□, □))

Explanation:

Step1: Find original coordinates

From the graph:

• \( T(-3, 1) \) (since it's 3 units left on x - axis, 1 unit up on y - axis)
• \( U(0, 1) \) (on y - axis, 1 unit up)
• \( V(0, 2) \) (on y - axis, 2 units up)
• \( W(-3, 2) \) (3 units left on x - axis, 2 units up)

Step2: Apply dilation rule

Dilation centered at origin with scale factor \( k \) transforms a point \( (x,y) \) to \( (kx,ky) \). Here \( k = 3 \).

For \( T(-3,1) \):

Multiply x and y by 3: \( T'(-3\times3,1\times3)=(-9,3) \)

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

Multiply x and y by 3: \( U'(0\times3,1\times3)=(0,3) \)

For \( V(0,2) \):

Multiply x and y by 3: \( V'(0\times3,2\times3)=(0,6) \)

For \( W(-3,2) \):

Multiply x and y by 3: \( W'(-3\times3,2\times3)=(-9,6) \)

Answer:

\( T'(-9, 3) \)
\( U'(0, 3) \)
\( V'(0, 6) \)
\( W'(-9, 6) \)