Question

janice plots △abc in the coordinate plane. her teacher asks her to rotate △abc 270° counterclockwise around the origin to form △abc. her original figure and its image are shown in the coordinate plane. use the drop - down menus to identify and correct janices error. instead of rotating △abc 270° counterclockwise around the origin, janice incorrectly rotated the figure. after a 270° counterclockwise rotation around the origin, the correct coordinates for the vertices of △abc should be a choose, b choose, and c choose.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Assume original coordinates

Let the original coordinates of the vertices of $\triangle ABC$ be $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$.

Step3: Apply rotation rule

The new coordinates $A'(y_1,-x_1)$, $B'(y_2,-x_2)$, $C'(y_3,-x_3)$ after a 270 - degree counter - clockwise rotation about the origin. Without the actual original coordinates given in the figure, we can't calculate the exact values, but this is the general method to correct the rotation.

Answer:

Use the rule $(x,y)\to(y, - x)$ to find the correct coordinates of $A'$, $B'$, $C'$ after a 270 - degree counter - clockwise rotation about the origin.