Question

graph the image of trapezoid stuv after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

From graph: \(S(-2,-4)\), \(T(2,-4)\), \(U(2,3)\), \(V(0,3)\)

Step2: Apply dilation rule

Dilation center origin: \((x,y)\to(3x,3y)\)
\(S'=3\times(-2,-4)=(-6,-12)\)
\(T'=3\times(2,-4)=(6,-12)\)
\(U'=3\times(2,3)=(6,9)\)
\(V'=3\times(0,3)=(0,9)\)

Step3: Plot new points

Connect \(S'(-6,-12)\), \(T'(6,-12)\), \(U'(6,9)\), \(V'(0,9)\)

Answer:

The image of trapezoid \(STUV\) after dilation has vertices at \(S'(-6,-12)\), \(T'(6,-12)\), \(U'(6,9)\), \(V'(0,9)\) (plot these points and connect them to form the dilated trapezoid).