Question

graph the image of rectangle rstu after a dilation with a scale factor of 1/5, centered at the origin.

Explanation:

Step1: Find coordinates of original rectangle

Assume coordinates of rectangle \(RSTU\) are \(R(-10,-10)\), \(S(10,-10)\), \(T(10,5)\), \(U(-10,5)\)

Step2: Apply dilation formula

Dilation formula centered at origin is \((x,y)\to(\frac{1}{5}x,\frac{1}{5}y)\)
For \(R(-10,-10)\): \((\frac{1}{5}\times(-10),\frac{1}{5}\times(-10))=(-2,-2)\)
For \(S(10,-10)\): \((\frac{1}{5}\times10,\frac{1}{5}\times(-10))=(2,-2)\)
For \(T(10,5)\): \((\frac{1}{5}\times10,\frac{1}{5}\times5)=(2,1)\)
For \(U(-10,5)\): \((\frac{1}{5}\times(-10),\frac{1}{5}\times5)=(-2,1)\)

Step3: Plot new points

Plot points \((-2,-2)\), \((2,-2)\), \((2,1)\), \((-2,1)\) and connect them to form the dilated rectangle.

Answer:

The coordinates of the dilated rectangle are \(R'(-2,-2)\), \(S'(2,-2)\), \(T'(2,1)\), \(U'(-2,1)\). Plot these points on the graph and connect them.