triangle abc be rotated 270 degrees clockwise with the origin as the center of the rotation what is the rule

When you are dealing with rotations on a coordinate plane and you need to rotate an object such as a triangle 270 degrees clockwise about the origin, there is a specific rule you can follow to find the new coordinates of each point after the rotation.

For a 270-degree clockwise rotation, each point of the triangle (x, y) will be transformed into a new point (x', y') following this rule:

(x', y') = (y, -x)

What this means is that the x-coordinate of the point after rotation becomes the opposite of the original y-coordinate, and the y-coordinate after the rotation becomes the original x-coordinate.

This rule is a result of the composition of rotations in the plane. Normally, a 90-degree clockwise rotation would transform any point (x, y) to (-y, x). However, three consecutive 90-degree clockwise rotations (or a single 270-degree clockwise rotation) would lead to the point (-y, x) being rotated two more times:

After the first 90-degree rotation: (x, y) → (-y, x)
After the second 90-degree rotation: (-y, x) → (-x, -y)
After the third 90-degree rotation: (-x, -y) → (y, -x)

So, for any point on triangle ABC, you can apply this transformation to get the new coordinates. Repeat this for all vertices of the triangle to find the vertices of the new, rotated triangle.