If AB = 28 inches then find the distance of A'B' after a reflection over the x-axis and a translation of (x + 7, y - 5)

To find the distance of A'B' after a reflection over the x-axis and a translation of (x + 7, y - 5), we need to perform the following steps:

1. Reflect point A (-28,0) over the x-axis, resulting in A' (28,0).
2. Translate A' by (x + 7, y - 5), resulting in A'B'.

The translation of (x + 7, y - 5) means we need to add 7 to the x-coordinate and subtract 5 from the y-coordinate.

So, the new coordinates of A' after the translation are (28 + 7, 0 - 5) = (35, -5).

Now, we need to calculate the distance between A' (35, -5) and the origin (0,0) using the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(0 - 35)^2 + (0 - (-5))^2]
Distance = √[(-35)^2 + 5^2]
Distance = √(1225 + 25)
Distance = √1250
Distance ≈ 35.36 inches

Therefore, the distance of A'B' after a reflection over the x-axis and a translation of (x + 7, y - 5) is approximately 35.36 inches.