Answer:
R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new position. Types of transformation include dilation, reflection, translation and rotation.
If a point A(x, y) is reflected over the line y = x, the new point is at A'(y, x)
If a point A(x, y) is rotated 180° clockwise about the origin, the new location is at A'(-x, -y)
Since Quadrilateral RAPS is located at the vertices R(-4,1), A(-3, 4), P(0,5), S(-1,1), After been reflected across the line y = x, the new locations are at:
R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1)
Then the rotation of the points R'(1, -4), A'(4, -3), P'(5, 0), S'(1, -1) 180° about the origin gives:
R''(-1, 4), A''(-4, 3), P''(-5, 0), S''(-1, 1)
![\begin{gathered} f(19)=\frac{3}{19+2}-\sqrt[]{19-3}, \\ \\ f(19)=\frac{3}{21}-\sqrt[]{16}, \\ \\ f(19)=\frac{1}{7}-4, \\ \\ f(19)=\frac{1-28}{7}, \\ \\ f(19)=-\frac{27}{7}\text{.} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%2819%29%3D%5Cfrac%7B3%7D%7B19%2B2%7D-%5Csqrt%5B%5D%7B19-3%7D%2C%20%5C%5C%20%20%5C%5C%20f%2819%29%3D%5Cfrac%7B3%7D%7B21%7D-%5Csqrt%5B%5D%7B16%7D%2C%20%5C%5C%20%20%5C%5C%20f%2819%29%3D%5Cfrac%7B1%7D%7B7%7D-4%2C%20%5C%5C%20%20%5C%5C%20f%2819%29%3D%5Cfrac%7B1-28%7D%7B7%7D%2C%20%5C%5C%20%20%5C%5C%20f%2819%29%3D-%5Cfrac%7B27%7D%7B7%7D%5Ctext%7B.%7D%20%5Cend%7Bgathered%7D)
Answer