Question

Suppose a linear transformation Upper T : Bold Upper R squared right arrow Bold Upper R squared is formed by taking a rotation counterclockwise of 180​ degrees, followed by a reflection across the Bold x 2​-axis. Describe the points that will be moved back to their original position by this​ transformation?

Answer 1

Answer:

All points on line x+y = 0 or x-y=0 will satisfy the transformation.

Step-by-step explanation:

Let (x, y) be the general such point.

Hence rotating it by 180 deg. counterclockwise will give us (-y,-x).

Reflecting (-y,-x) on x axis gives us (-y,x).

Hence if (x,y) = (-y,x) then all ( x, y) where x = -y or x+y = 0 or x=y or x-y=0 will satisfy this condition.

All points on line x+y = 0 or x-y=0 will satisfy the transformation.