Final answer:
Triangle A'B'C' is formed by a reflection over x = -3 and dilation by a scale factor of 3 from the origin. The correct equation that shows the relationship between ΔABC and ΔA'B'C' is d) All of the above.
Step-by-step explanation:
To find the correct relationship between ΔABC and ΔA'B'C', we need to understand the transformations that have been applied. The triangle A'B'C' is formed by a reflection over the line x = -3 and a dilation by a scale factor of 3 from the origin.
When we reflect a point over the line x = -3, the x-coordinate stays the same, but the y-coordinate becomes its negative. So, (x, y) becomes (x, -y).
After the reflection, we dilate the triangle by a scale factor of 3 from the origin, which means that each coordinate is multiplied by 3. Therefore, the coordinates of A', B', and C' are (3x, -3y), (3x, -3y), and (3x, -3y) respectively.
The correct equation that shows the relationship between ΔABC and ΔA'B'C' is d) All of the above. This is because all three sides of the triangle are multiplied by a scale factor of 3 in the dilation process, which means that AB = 3A'B', BC = 3B'C', and AC = 3A'C'.