Question

If point Q coordinates are four and -7 and its rotated 270° counterclockwise about five and one what is the coordinates of

Answer 1

To find the new coordinates of point Q after a 270° counterclockwise rotation around the point (5, 1), translate point Q to the origin, apply the rotation, and translate back. The new coordinates are (13, 2).

Step-by-step explanation:

The question asks for the new coordinates of a point after it has been rotated 270° counterclockwise about another point. To find the coordinates after rotation, one can apply the rotation matrix or use a geometric approach. Here, we'll use a geometric strategy to determine the new position of point Q (4, -7) after a 270° counterclockwise rotation about pivot point (5, 1).

Steps to Find the Coordinates after 270° Rotation

1. Translate point Q so that the pivot point is at the origin: (Q.x - pivot.x, Q.y - pivot.y) = (4 - 5, -7 - 1) = (-1, -8).
2. Apply the 270° counterclockwise rotation to translated point: for 270°, we switch the coordinates and change the sign of the new x-coordinate, which yields (8, 1).
3. Translate the point back to the original position by adding the pivot point's coordinates: (8 + 5, 1 + 1) = (13, 2).

The new coordinates of point Q after a 270° counterclockwise rotation about the point (5, 1) are (13, 2).