Question

the rectangle ijkl is a dilation of the rectangle ijkl. what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a side of the original rectangle

The length of \(IL\) (original rectangle \(IJKL\)): \(I(-10,1)\), \(L(10,1)\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d=\vert10-(- 10)\vert = 20\).

Step2: Find the length of the corresponding side of the dilated rectangle

The length of \(I'L'\) (dilated rectangle \(I'J'K'L'\)): \(I'(-5,1)\), \(L'(5,1)\). Using the distance formula for horizontal line \(d=\vert x_2 - x_1\vert\), \(d=\vert5-(-5)\vert = 10\).

Step3: Calculate the scale factor

The scale factor \(k=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). So \(k=\frac{10}{20}=\frac{1}{2}\).

Answer:

The scale factor of the dilation is \(\frac{1}{2}\)