Question

qr is the image of qr after a dilation by a scale factor of 3 centered at the origin. what is the length of qr?

Explanation:

Step1: Find the length of \( \overline{QR} \)

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
For \( Q(3,0) \) and \( R(0,4) \), \( x_1 = 0,y_1 = 4,x_2 = 3,y_2 = 0 \).
\( QR=\sqrt{(3 - 0)^2+(0 - 4)^2}=\sqrt{9 + 16}=\sqrt{25}=5 \).

Step2: Use the property of dilation

If the scale factor is \( k = 3 \), and the length of the original segment is \( l\), the length of the dilated segment \( l'=k\times l \).
Since \( l = QR = 5\) and \( k = 3 \), then \( Q'R'=3\times5 \).

Answer:

\( 15 \)