Question

1. the rectangle below is the result of a dilation. if the scale factor used in the dilation was 2, what were the side lengths of the original figure? 40 cm 28 cm

Explanation:

Step1: Recall the formula for dilation

The formula for dilation is \( \text{Image length}=\text{Scale factor}\times\text{Original length}\). So, \( \text{Original length}=\frac{\text{Image length}}{\text{Scale factor}}\).

Step2: Calculate the original length for the side of \(40\) cm

Given the scale factor \(k = 2\) and image length \(l_{image}=40\) cm. Using the formula \(l_{original}=\frac{l_{image}}{k}\), we have \(l_{original}=\frac{40}{2}=20\) cm.

Step3: Calculate the original length for the side of \(28\) cm

Given the scale factor \(k = 2\) and image length \(w_{image}=28\) cm. Using the formula \(w_{original}=\frac{w_{image}}{k}\), we have \(w_{original}=\frac{28}{2}=14\) cm.

Answer:

The side - lengths of the original rectangle were \(20\) cm and \(14\) cm.