Final answer:
The relationship between ΔABC and ΔA″B″C″ is achieved by applying a reflection over y = -3 and a dilation by a scale factor of 2, resulting in the transformation equation (x, y) → (2x, -2y-12).
Step-by-step explanation:
The relationship between ΔABC and ΔA″B″C″, wherein ΔA″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin, is expressed through a combination of transformation equations. First, the reflection over the line y = −3 can be represented by the transformation (x, y) → (x, -y-6), which flips the point over the line y = −3. Subsequently, the dilation from the origin by a scale factor of 2 can be represented by the transformation (x, y) → (2x, 2y). Therefore, for any point (x, y) in ΔABC, the corresponding point in ΔA″B″C″ would be (2x, -2y-12) after applying both transformations in sequence.