Question

△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 check box. the distance between the y-coordinates of r and t is check box. r is dropdown from t, so the coordinates of r are dropdown.

Explanation:

Step1: Find coordinates of R

From the graph, R is at (0, 4). T is at (3, -2).

Step2: Distance between x - coordinates

The x - coordinate of R is 0, x - coordinate of T is 3. Distance is \(|3 - 0|=3\).

Step3: Distance between y - coordinates

The y - coordinate of R is 4, y - coordinate of T is - 2. Distance is \(|4-(-2)| = |4 + 2|=6\).

Step4: Dilation factor and new distances

Dilation rule is \(D_{T,1/3}(x,y)\), so scale factor \(k=\frac{1}{3}\). New x - distance from T: \(3\times\frac{1}{3}=1\), new y - distance from T: \(6\times\frac{1}{3}=2\).

Step5: Coordinates of R'

Since T is (3, - 2), to find R', we move 1 unit in x - direction (from T's x - coordinate: \(3-1 = 2\)) and 2 units in y - direction (from T's y - coordinate: \(-2 + 2=0\)). So R' is \((2,0)\). Also, R' is \(\frac{1}{3}\) the distance from T as R is.

Answer:

• Distance between x - coordinates of R and T: 3
• Distance between y - coordinates of R and T: 6
• R' is \(\frac{1}{3}\) the distance from T
• Coordinates of R': \((2,0)\)