What is the translation of the point to its image? A (−1, 4)→ A' (3, 3)

We validate that the formula to determine the translation of the point to its image will be:

A (x, y) → A' (x+4, y-1)

Step-by-step explanation:

Given

A (−1, 4)→ A' (3, 3)

Here:

We need to determine which translation operation brings the coordinates of the image A'(3, 3).

If we closely observe the coordinates of the image A' (3, 3), it is clear the image coordinates can be determined by adding 4 units to the x-coordinate and subtracting 1 unit to the y-coordinate.

Thue, the rule of the translation will be:

A(x, y) → A' (x+4, y-1)

Let us check whether this translation rule validates the image coordinates.

A (x, y) → A' (x+4, y-1)

Given that A(-1, 4), so

A (-1, 4) → A' (-1+4, 4-1) = A' (3, 3)

Therefore, we validate that the formula to determine the translation of the point to its image will be:

A (x, y) → A' (x+4, y-1)