If __AB = 27 in then find the distance of a __A'B' after a reflection over the x-axis and a translation of
(x + 6, y -2)
To find the distance of A'B', we first need to determine the coordinates of A' and B' after the given transformations.
1. Reflection over the x-axis:
The reflection over the x-axis changes the sign of the y-coordinate. So, the new coordinates of A and B would be (A.x, -A.y) and (B.x, -B.y), respectively.
2. Translation of (x + 6, y - 2):
The translation shifts the coordinates of A' and B' by +6 units in the x-direction and -2 units in the y-direction. So, the new coordinates of A' and B' would be (A.x + 6, -A.y - 2) and (B.x + 6, -B.y - 2), respectively.
To find the distance of A'B', use the distance formula:
d = √[(A'.x - B'.x)^2 + (A'.y - B'.y)^2]
Substituting the new coordinates, we get:
d = √[(A.x + 6 - B.x - 6)^2 + (-A.y - 2 - (-B.y - 2))^2]
= √[(A.x - B.x)^2 + (A.y - B.y)^2]
Since AB = 27 in, the distance of A'B' would also be 27 in, as the transformations involved do not affect the distance between the points.