Question

rectangle fghij is dilated according to the rule d_{o,\frac{1}{3}} to create the image rectangle fghj, which is shown on the graph.
where is point f of the pre - image located?
plot the point on the coordinate grid.

Explanation:

Step1: Determine the coordinates of the image point \(F'\)

From the graph, the coordinates of \(F'\) are \((2,3)\).

Step2: Use the dilation rule \(D_{o,\frac{1}{3}}\)

The dilation rule \(D_{o,k}\) (where \(o\) is the origin \((0,0)\) and \(k = \frac{1}{3}\)) for a point \((x',y')\) of the image is related to the pre - image point \((x,y)\) by the formula \((x',y')=(k x,k y)\). Let the pre - image point \(F=(x,y)\). Then \(x' = 2=\frac{1}{3}x\) and \(y' = 3=\frac{1}{3}y\).

Step3: Solve for \(x\) and \(y\)

If \(2=\frac{1}{3}x\), then \(x = 6\) (by multiplying both sides of the equation \(2=\frac{1}{3}x\) by \(3\)). If \(3=\frac{1}{3}y\), then \(y = 9\) (by multiplying both sides of the equation \(3=\frac{1}{3}y\) by \(3\)).

Answer:

The coordinates of the pre - image point \(F\) are \((6,9)\)