Question

the trapezoid ( opqr ) is a dilation of the trapezoid ( opqr ). what is the scale factor of the dilation?

Explanation:

Step1: Find the length of a corresponding side

Let's take side \(QR\) and \(Q'R'\).
The length of \(QR\): \(QR = 6 - (- 5)=11\) (using the distance formula for horizontal line \(y = 10\), \(x\) - coordinates of \(Q(-5,10)\) and \(R(6,10)\)).
The length of \(Q'R'\): \(Q'R'=4 - (- 4)=8\) (using the distance formula for horizontal line \(y = 8\), \(x\) - coordinates of \(Q'(-4,8)\) and \(R'(4,8)\)).
Wait, no, better use the ratio of vertical or horizontal distances from the center of dilation (origin in this case).
Take point \(Q(-5,10)\) and \(Q'(-4,8)\).
The scale factor \(k\) for dilation \((x,y)\to(kx,ky)\).
For \(y\) - coordinate: \(k=\frac{y'}{y}\), \(y = 10\) (of \(Q\)), \(y'=8\) (of \(Q'\)).

Step2: Calculate the scale factor

\(k=\frac{8}{10}=\frac{4}{5}\)

Answer:

\(\frac{4}{5}\)