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

First, identify the original coordinates of each vertex from the graph:

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

Step2: Apply dilation rule

The rule for dilation centered at the origin with scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here, \( k = 3 \).

For \( T(-3,1) \):
Multiply x and y by 3: \( T'=(3\times(-3),3\times1)=(-9,3) \)

For \( U(0,1) \):
Multiply x and y by 3: \( U'=(3\times0,3\times1)=(0,3) \)

For \( V(0,2) \):
Multiply x and y by 3: \( V'=(3\times0,3\times2)=(0,6) \)

For \( W(-3,2) \):
Multiply x and y by 3: \( W'=(3\times(-3),3\times2)=(-9,6) \)

Answer:

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