If AB = 21 inches then find the distance of A'B'after a reflection over the x-axis and a rotation of 337° clockwise.

To find the distance of A'B' after a reflection over the x-axis and a rotation of 337° clockwise, we need to first find the coordinates of A' and B' after the reflection over the x-axis.

Given AB = 21 inches, let A = (0,0) and B = (0,21).

After reflecting over the x-axis, A' will remain the same (0,0) and B' will be (-21,0).

Next, we need to rotate B' by 337° clockwise. Rotating a point (x,y) by θ degrees clockwise results in a new point given by:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

Plugging in the values, we get:
x' = -21*cos(337°) - 0*sin(337°) ≈ -14.56
y' = -21*sin(337°) + 0*cos(337°) ≈ 16.68

Therefore, the coordinates of B' after the rotation are approximately (-14.56, 16.68).

Using the distance formula, which is √((x2-x1)^2 + (y2-y1)^2), we can find the distance between A' and B':
√((-14.56-0)^2 + (16.68-0)^2) ≈ √(212.2436) ≈ 14.57 inches

Therefore, the distance of A'B' after the reflection over the x-axis and a rotation of 337° clockwise is approximately 14.57 inches.