Question

quadrilateral e is a scaled copy of quadrilateral d. what scale factor takes quadrilateral d to quadrilateral e?

Explanation:

Step1: Determine the scale factor formula

The scale factor \(k\) from the original figure (quadrilateral \(D\)) to the scaled - copy (quadrilateral \(E\)) is given by \(k=\frac{\text{length of a side in }E}{\text{length of the corresponding side in }D}\).

Step2: Identify corresponding sides

We can use the sides of length \(12\) in quadrilateral \(D\) and \(8\) in quadrilateral \(E\) (or the sides of length \(8\) in quadrilateral \(D\) and \(5\) in quadrilateral \(E\)). Using the sides \(12\) (in \(D\)) and \(8\) (in \(E\)):
\(k = \frac{8}{12}\)

Step3: Simplify the fraction

Simplify \(\frac{8}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(4\). \(\frac{8\div4}{12\div4}=\frac{2}{3}\)

Answer:

The scale factor is \(\frac{2}{3}\)