The point a(-8, 6) is translated using t: (x, y) → (x + 5. y - 4). what is the distance from a to a'?

Translated means the points are moving across the plane without rotating or changing shape. In this case, the x-coordinate would be moving up 5 (x + 5) and the y-coordinate would be moving to the left 4 (y - 4).

A is (-8, 6). A' is the result of the translation from this point. The results of the solution above in A is the point (-3, 2) = A'.

Now you must find the distance between these two coordinates. To find the distance you must use the distance formula: √(x2 - x1)^2 + (y2 - y1)^2. Since you now have two points, A and A', plug these into the distance formula.

√(-3 - (-8))^2 + (2 - 6)^2
√5^2 + (-4)^2
√25 + 16
√41

The distance from A to A' is √41.