Question

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

Explanation:

Step1: Find original coordinates

From the graph, \( R(-1, -1)\), \( S(-1, 1)\), \( T(0, 3)\), \( U(1, 1)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = 3\), the formula is \((x,y)\to(kx,ky)\)

• For \(R(-1,-1)\): \((-1\times3,-1\times3)=(-3,-3)\)
• For \(S(-1,1)\): \((-1\times3,1\times3)=(-3,3)\)
• For \(T(0,3)\): \((0\times3,3\times3)=(0,9)\)
• For \(U(1,1)\): \((1\times3,1\times3)=(3,3)\)

Answer:

\( R(-3,-3)\), \( S(-3,3)\), \( T(0,9)\), \( U(3,3)\)