Question

Write a rule for the given transformation. PLEASE HELP a. rotation 180° about the origin b. translation (x,y) -> (x +6, y+2) c. rotation 90° clockwise about the origin d. rotation 90° counterclockwise about the origin.

Answer 1

To rotate a shape about the origin 90° clockwise, switch the x and y values for each vertex of the figure and then multiply the new x-value by -1, like this:

(x,y) -> (-y,x)

In this case, we go from the rectangle whose vertices are located at (2,2), (2,5), (8,2) and (8,5), when we rotate these points about the origin 90° clockwise, we get:

(2,2) -> (-2,2)

(2,5) -> (-5,2)

(8,2) -> (-2,8)

(8,5) -> (-5,8)

When we graph these points we get:

As you can see, the new shape looks the same as the one given in the question, then we have proved that the correct answer is option c, a rotation 90° clockwise about the origin.