13 after a reflection of the x axis and a rotation of 50 degrees clockwise
To perform a reflection of a point (x, y) across the x-axis, the new coordinates become (x, -y).
After the reflection across the x-axis, the new coordinates become (13, -13).
To perform a rotation of 50 degrees clockwise, we can use the following rotation matrix:
| cosθ sinθ |
| -sinθ cosθ |
In this case, θ = -50 degrees since we want a clockwise rotation. Converting -50 degrees to radians, we have -50 * (π/180) = -5π/18.
Applying the rotation matrix to the reflected point (13, -13), we get:
| cos(-5π/18) sin(-5π/18) | | 13 | | -11.049 |
| -sin(-5π/18) cos(-5π/18) | x | -13 | = | -5.336 |
Therefore, after a reflection across the x-axis and a rotation of 50 degrees clockwise, the new coordinates of the point (13, -13) are approximately (-11.049, -5.336).