What is the final position of point (7,8) after a translation of 2 units left, 1 unit down, and followed by a 180 degree clockwise rotation around the origin?
To find the final position of a point after a translation and rotation, we need to perform each operation in order.
First, let's apply the translation of 2 units left and 1 unit down. This means we subtract 2 from the x-coordinate and subtract 1 from the y-coordinate.
After the translation, the new coordinates of point (7,8) are (7-2, 8-1), which simplifies to (5,7).
Next, let's apply the 180 degree clockwise rotation around the origin. To achieve this, we change the sign of both the x and y-coordinates.
After the rotation, the final coordinates of point (5,7) become (-5,-7).
Therefore, the final position of point (7,8) after a translation of 2 units left, 1 unit down, and a 180 degree clockwise rotation around the origin is (-5,-7).