How should one find the image of a point under a series of transformations?

To find the image of a point under a series of transformations, one should apply the transformations sequentially. This approach involves taking the point and first applying the initial transformation to obtain a new point, then using this resulting point as the starting point for the next transformation, and so on. Following this order is essential because transformations like translation, rotation, scaling, and reflection can yield different results based on the sequence in which they are applied. Each transformation is dependent on the position of the point after the previous transformation has been executed.

By applying transformations sequentially, you ensure that each transformation acts on the most current position of the point, which accurately reflects the cumulative effect of the entire series of transformations. This method aligns with the mathematical principles governing transformations in geometry, allowing for correct and expected outcomes based on the ordered application of operations.