If AB= 27 inches, then find the distance of A'B' after a reflection over the x axis and a translation of (x + 6, y - 2)
To find the distance of A'B' after the reflection over the x-axis and translation of (x + 6, y - 2), we need to first consider the effects of the reflection and translation on the coordinates of A and B.
1. Reflection over the x-axis: This means the y-coordinate of each point switches its sign while the x-coordinate remains the same. Let's say the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2). After the reflection, the new coordinates will be (x1, -y1) for A' and (x2, -y2) for B'.
2. Translation of (x + 6, y - 2): This means we add 6 to the x-coordinate and subtract 2 from the y-coordinate. After the translation, the new coordinates of A' and B' will be (x1 + 6, -y1 - 2) and (x2 + 6, -y2 - 2) respectively.
Now that we have the coordinates of A' and B', we can use the distance formula to find the distance between them:
distance = √((x2 + 6 - x1 - 6)^2 + (-y2 - 2 - (-y1 - 2))^2)
= √((x2 - x1)^2 + (-y2 + y1)^2)
Since AB = 27 inches, the distance between the original points A and B is 27 inches. This can be expressed as:
distance = √((x2 - x1)^2 + (-y2 + y1)^2) = 27
Note: The actual numerical value of the distance cannot be determined without the specific coordinates of A and B.