If

AB
=
12 inches then find the distance of
A

B

after a reflection over the x-axis and a translation of
(x+4, y−9)

=A ′ B ′ = inches

1 answer

To find the distance of A' B' after the reflection over the x-axis, we first need to find the coordinates of A' and B' after the reflection.

For A', the x-coordinate remains the same, while the y-coordinate changes its sign. Since A is located on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A' after the reflection over the x-axis are (x, -y).

For B', the x-coordinate remains the same, while the y-coordinate changes its sign. Since B is located on the positive y-axis, its y-coordinate is positive. Therefore, the coordinates of B' after the reflection over the x-axis are (x, -y).

Next, we need to perform the translation of (x+4, y-9) on the coordinates of A' and B'.

The coordinates of A' after the translation are (x+4, -y-9).
The coordinates of B' after the translation are (x+4, -y-9).

To find the distance between A' and B', we use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((x+4 - x+4)^2 + ((-y-9) - (-y-9))^2)

Distance = √(0^2 + 0^2)

Distance = √0

Distance = 0 inches