Question

the rectangle ( ijkl ) is a dilation of the rectangle ( ijkl ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

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

The length of \(KL\) (original rectangle \(IJKL\)): \(K(8,10)\), \(L(8,2)\). Using the distance formula for vertical points (since \(x -\)coordinates are the same), \(d=\vert y_2 - y_1\vert\). So \(KL=\vert10 - 2\vert=8\).

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

The length of \(K'L'\) (dilated rectangle \(I'J'K'L'\)): \(K'(4,5)\), \(L'(4,1)\). Using the distance formula for vertical points (since \(x -\)coordinates are the same), \(d=\vert y_2 - y_1\vert\). So \(K'L'=\vert5 - 1\vert = 4\).

Step3: Calculate the scale factor

The scale factor \(s\) of a dilation is given by \(s=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). So \(s=\frac{K'L'}{KL}=\frac{4}{8}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)