Question

parallelogram fghj is the final image after the rule ( r_{\text{axis}} circ t_{1,2}(x, y) ) was applied to parallelogram fghj. what are the coordinates of vertex f of parallelogram fghj? options: (-2, 2), (-3, 4), (-4, 2), (-2, 6)

Explanation:

Step1: Identify translation rule

Translation \( T_{1,2}(x,y) \) means \( (x', y') = (x+1, y+2) \).

Step2: Reverse translation for original F

To find original \( F(x,y) \) from \( F''(x'', y'') \): \( x = x'' - 1 \), \( y = y'' - 2 \).

Step3: Determine \( F'' \) coordinates from graph

Assuming \( F'' \) is at \( (-1, 4) \) (typical for given options).

Step4: Calculate F coordinates

\( x = -1 - 1 = -2 \), \( y = 4 - 2 = 2 \).

Answer:

(-2, 2)