Question

graph the image of trapezoid ( rstu ) after a dilation with a scale factor of ( \frac{1}{5} ), centered at the origin. save answer

Explanation:

Step1: Identify the coordinates of trapezoid \(RSTU\)

• \(R(- 5,-9)\)
• \(S(-5,-5)\)
• \(T(5,5)\)
• \(U(5,-9)\)

Step2: Apply the dilation formula

The dilation formula for a point \((x,y)\) with a scale factor \(k=\frac{1}{5}\) centered at the origin \((0,0)\) is \((x',y')=(kx,ky)\)

• For \(R(-5,-9)\): \(x'=\frac{1}{5}\times(-5)=-1\), \(y'=\frac{1}{5}\times(-9)=-\frac{9}{5}=-1.8\)
• For \(S(-5,-5)\): \(x'=\frac{1}{5}\times(-5)=-1\), \(y'=\frac{1}{5}\times(-5)=-1\)
• For \(T(5,5)\): \(x'=\frac{1}{5}\times5 = 1\), \(y'=\frac{1}{5}\times5=1\)
• For \(U(5,-9)\): \(x'=\frac{1}{5}\times5 = 1\), \(y'=\frac{1}{5}\times(-9)=-\frac{9}{5}=-1.8\)

Step3: Plot the new points

Plot the points \(R'(-1,-1.8)\), \(S'(-1,-1)\), \(T'(1,1)\), \(U'(1,-1.8)\) and connect them to form the dilated trapezoid.

Answer:

The coordinates of the dilated trapezoid are \(R'(-1,-1.8)\), \(S'(-1,-1)\), \(T'(1,1)\), \(U'(1,-1.8)\). Plot these points on the coordinate - plane and connect them.