Question

graph the image of rectangle rstu after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Find the coordinates of the original rectangle

Assume the coordinates of rectangle \(RSTU\) are \(R(-10,-10)\), \(S(10,-10)\), \(T(10,5)\), \(U(-10,5)\) (estimated from the graph).

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(\frac{1}{5}x,\frac{1}{5}y)\).

• For point \(R(-10,-10)\): \((\frac{1}{5}\times(-10),\frac{1}{5}\times(-10))=(-2,-2)\)
• For point \(S(10,-10)\): \((\frac{1}{5}\times10,\frac{1}{5}\times(-10))=(2,-2)\)
• For point \(T(10,5)\): \((\frac{1}{5}\times10,\frac{1}{5}\times5)=(2,1)\)
• For point \(U(-10,5)\): \((\frac{1}{5}\times(-10),\frac{1}{5}\times5)=(-2,1)\)

Step3: Plot the new points

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

Answer:

The image of rectangle \(RSTU\) after dilation has vertices at \((-2,-2)\), \((2,-2)\), \((2,1)\), \((-2,1)\). Graph these points and connect them to get the dilated rectangle.