Question

qr is graphed below. 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? units

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 \( R(0,4) \), \( x_1 = 3,y_1 = 0,x_2 = 0,y_2 = 4 \).

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Step2: Use the property of dilation

Since \( \overline{Q'R'} \) is the image of \( \overline{QR} \) after a dilation by a scale factor \( k = 3 \) centered at the origin. The length of the image of a line segment after dilation is \( d'=k\times d \). Here \( d = QR = 5,k = 3 \).
So \( Q'R'=3\times QR \)

$$Q'R'=3\times5 = 15$$

Answer:

15