Question

quadrilateral qrst is dilated and translated to form similar figure qrst. what is the scale factor for the dilation?

Explanation:

Step1: Identify Corresponding Sides

First, find the length of a side in the original quadrilateral \( QRST \) and the corresponding side in the dilated quadrilateral \( Q'R'S'T' \). Let's take the vertical side \( QR \) and \( Q'R' \). From the grid, \( QR \) has a length of \( 4 \) units (from \( y = -4 \) to \( y = 0 \) or similar, depending on grid). \( Q'R' \) has a length of \( 2 \) units.

Step2: Calculate Scale Factor

The scale factor \( k \) of a dilation is the ratio of the length of a side in the image (\( Q'R'S'T' \)) to the length of the corresponding side in the pre - image (\( QRST \)). So \( k=\frac{\text{Length of }Q'R'}{\text{Length of }QR}=\frac{2}{4}=\frac{1}{2} \). Or we can also check another side, say the horizontal or slant side, and we will get the same ratio.

Answer:

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