Given:
The point P(-2, - 5) is rotated 90° about the origin, and then the image is reflected across the line x= 3.
To find:
The the coordinates of the final image P’’.
Solution:
The point P(-2, - 5) is rotated 90° about the origin. It means the point is rotated 90° counter clockwise about the origin
[tex](x,y)\to (-y,x)[/tex]
[tex]P(-2,-5)\to P'(-(-5),(-2))[/tex]
[tex]P(-2,-5)\to P'(5,-2)[/tex]
Then the image is reflected across the line x= 3.
[tex](x,y)\to (-x+6,y)[/tex]
[tex]P'(5,-2)\to P''(-5+6,-2)[/tex]
[tex]P'(5,-2)\to P''(1,-2)[/tex]
Therefore, the \coordinates of the final image P'' are (1,-2).
