Question

destiny plots lepg in the coordinate plane. then destinys teacher asks her to rotate lepg 90° clockwise around the origin to form its image lepg. her original figure and image are shown in the coordinate plane.
a. what error did destiny make?
b. what are the correct coordinates of the vertices for the image?
c. draw the correct image lepg in the coordinate plane.

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Identify error

Without seeing the actual work, a common error is using the wrong rotation rule, like rotating 90 - degree clockwise ($(x,y)\to(y, - x)$) instead of counter - clockwise.

Step3: Find correct coordinates

Let the original vertices of the figure be $(x_1,y_1),(x_2,y_2),\cdots$. Apply the rule $(x,y)\to(-y,x)$ to each vertex to get the new coordinates.

Step4: Draw the image

Plot the new vertices on the coordinate plane and connect them to form the rotated figure.

Answer:

a. A common error could be using the wrong rotation rule (e.g., rotating 90 - degree clockwise instead of counter - clockwise).
b. Without the original coordinates, we can't give specific values. But use the rule $(x,y)\to(-y,x)$ for each vertex.
c. After finding the correct coordinates in part b, plot the vertices and connect them to draw the figure.