Given:
Point (7,12) is rotated 1260° counterclockwise about the origin.
To find:
The x-coordinate of the point after this rotation.
Solution:
If a point is rotated 360 degrees then its coordinates remains unchanged.
If a point is rotated 180 counterclockwise about the origin degrees, then
[tex](x,y)\to (-x,-y)[/tex]
We know that,
[tex]1260^\circ=1080^\circ+180^\circ[/tex]
[tex]1260^\circ=3\times 360^\circ+180^\circ[/tex]
After [tex]3\times 360^\circ[/tex] rotation the coordinates of points remains same, i.e., (7,12). So, after that (7,12) is rotated 180° counterclockwise about the origin.
[tex](7,12)\to (-7,-12)[/tex]
The point (7,12) becomes (-7,-12) after rotation of 1260° counterclockwise about the origin.
Therefore, the x-coordinate of the required point is -7.
