Question

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

Explanation:

Step1: Determine the length of QR and QT

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

Step2: Calculate the length of the dilated sides

Since the scale factor \(k = 3\), for a dilation centered at \(Q\), the length of the dilated side \(Q'R'\) (where \(Q'\) coincides with \(Q\)) is \(QR\times k\) and \(Q'T'\) is \(QT\times k\).
For side \(QR\): \(QR\times k=2\times3 = 6\)
For side \(QT\): \(QT\times k=2\times3=6\)

Step3: Construct the dilated rectangle

Since \(Q\) is the center of dilation, \(Q\) remains in the same position. Draw a line segment from \(Q\) with length \(6\) in the direction of \(QR\) (vertical direction) and in the direction of \(QT\) (horizontal direction). Then complete the rectangle.

Answer:

The dilated rectangle will have sides of length \(6\) (corresponding to the original sides of length \(2\)) with \(Q\) as one of its vertices.