If AB = 22 inches then find the distance of A'B' after a reflection over the x-axis and a translation of (x+4,y-7)
To find the distance of A'B' after a reflection over the x-axis and a translation of (x+4, y-7), we need to understand the transformation steps involved.
1. Reflection over the x-axis: This involves flipping the shape or object over the x-axis. In this case, the y-coordinate of a point A is negated. So the point A' after reflection over the x-axis will have the same x-coordinate as A, but its y-coordinate will be -y.
2. Translation: This involves moving the shape or object by a certain distance horizontally (x-axis) and vertically (y-axis). In this case, we're translating the shape by (x+4, y-7), which means moving x units to the right and y units down.
Applying these transformations to point A (0, 22):
1. Reflection over the x-axis: The y-coordinate changes its sign, so A' becomes (0, -22).
2. Translation: We move A' by (x+4, y-7), so the new coordinates of A' become (0 + 4, -22 - 7) = (4, -29).
Now, to find the distance between A'B', we calculate the distance between (0, 22) and (4, -29) using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 0)^2 + (-29 - 22)^2)
= √(4^2 + (-51)^2)
= √(16 + 2601)
= √(2617)
≈ 51.1591 inches
Therefore, the distance between A'B' after the reflection over the x-axis and translation (x+4, y-7) is approximately 51.1591 inches.