Question

dilate rectangle qrst by a scale factor of 3 with the center of dilation at point q.

Explanation:

planation:

Step1: Determine the length of \(QT\) and \(QR\)

Assume each grid unit is \(1\). From the figure, \(QT = 2\) units and \(QR=1\) unit.

Step2: Calculate the new lengths after dilation

Since the scale factor \(k = 3\), the new length of \(QT'\) (where \(T'\) is the image of \(T\)) is \(k\times QT=3\times2 = 6\) units, and the new length of \(QR'\) (where \(R'\) is the image of \(R\)) is \(k\times QR=3\times1=3\) units.

Step3: Construct the dilated rectangle

Starting from the center \(Q\), move \(6\) units along the line \(QT\) to get the new position of \(T\) (let's call it \(T'\)), and move \(3\) units along the line \(QR\) to get the new position of \(R\) (let's call it \(R'\)). Then, since it is a rectangle, we can find the new positions of \(S\) (call it \(S'\)) by using the properties of rectangles (opposite sides are equal and parallel).

Answer:

Construct a rectangle with sides \(QR' = 3\) units and \(QT'=6\) units (where \(Q\) is the center of dilation), maintaining the right - angle property of the rectangle.