If AB = 22 inches then find the distance of A'B' after a reflection over the x-axis and translation of (x+4,y-7)
To find the distance A'B' after a reflection over the x-axis, we need to find the y-coordinate of A'B'.
Since A'B' is a reflection of AB over the x-axis, the y-coordinate of A'B' will be -y, where y is the y-coordinate of AB.
To find the distance A'B' after the translation (x+4, y-7), we need to add the x-coordinate of the translation (which is 4) to the x-coordinate of A'B', and add the y-coordinate of the translation (which is -7) to the y-coordinate of A'B'.
Let's assume the x-coordinate of A'B' after the reflection over the x-axis is x1 and the y-coordinate of A'B' after the reflection over the x-axis is y1.
Therefore, we have the following coordinates for A' and B' after the reflection:
A' = (x1, -y1)
B' = (x1 + 22, -y1)
After the translation, the coordinates of A' and B' become:
A'' = (x1 + 4, -y1 - 7)
B'' = (x1 + 26, -y1 - 7)
The distance between A'' and B'' is given by the formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of A'' and B'', we have:
Distance = sqrt((x1 + 26 - x1 - 4)^2 + (-y1 - 7 - (-y1))^2)
= sqrt(22^2 + 7^2)
Therefore, the distance of A'B' after the reflection over the x-axis and translation of (x+4, y-7) is sqrt(22^2 + 7^2) inches.