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 3. the distance between the y-coordinates of r and t is 6. r is dropdown from t, so the coordinates of r dropdown options: 1 unit left, 1 unit up; 1 unit left, 2 units up; 3 units left, 2 units up; 2 units left, 4 units up

Explanation:

Step1: Find coordinates of R and T

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

Step2: Analyze dilation rule

Dilation rule \( D_{T, 1/3}(x, y) \) means scale factor \( \frac{1}{3} \) from center \( T \).
Distance in x - coordinates: \( |0 - 3| = 3 \), scaled distance: \( 3\times\frac{1}{3}=1 \) (left, since \( R \) is left of \( T \) in x - direction).
Distance in y - coordinates: \( |4 - (-2)| = 6 \), scaled distance: \( 6\times\frac{1}{3}=2 \) (up, since \( R \) is above \( T \) in y - direction).
So \( R' \) is 1 unit left, 2 units up from \( T \).

Answer:

1 unit left, 2 units up