Question

dilating a figure with the center of dilation at a point
△rst is dilated with the rule ( d_{t,1/3}(x,y) ), where the center of dilation is ( t(3,-2) ).
the distance between the x - coordinates of r and t is
the distance between the y - coordinates of r and t is
( r ) is from t, so the coordinates of ( r )

Explanation:

Step1: Find coordinates of \(R\)

From the graph, \(R=(0,4)\) and \(T=(3, - 2)\)

Step2: Calculate the change in \(x\) and \(y\) after dilation

The dilation rule is \(D_{T,\frac{1}{3}}(x,y)\).
The change in \(x\) - coordinate between \(R\) and \(T\) is \(0 - 3=-3\). After dilation, the change in \(x\) - coordinate is \(-3\times\frac{1}{3}=-1\) (1 unit left).
The change in \(y\) - coordinate between \(R\) and \(T\) is \(4-(-2) = 6\). After dilation, the change in \(y\) - coordinate is \(6\times\frac{1}{3}=2\) (2 units up).

Answer:

1 unit left, 2 units up