Question

the shape above has the following coordinates. rotate the shape 180° counter - clockwise. what are the coordinates of the image? (x, y)→(opposite of y, x) (3, 2)→(-2, 3) (x, y)→(-y, x) 90° ccw or 270° cw change the y and flip

Explanation:

Step1: Recall 180 - degree rotation rule

The rule for rotating a point $(x,y)$ 180 - degrees counter - clockwise about the origin is $(x,y)\to(-x,-y)$.

Step2: Assume coordinates of points

Let's assume the coordinates of point $R$ are $(x_R,y_R)$ and of point $Y$ are $(x_Y,y_Y)$ and of point $B$ are $(x_B,y_B)$.

Step3: Apply the rotation rule to point $R$

If $R=(x_R,y_R)$, then $R'=(-x_R,-y_R)$.

Step4: Apply the rotation rule to point $Y$

If $Y=(x_Y,y_Y)$, then $Y'=(-x_Y,-y_Y)$.

Step5: Apply the rotation rule to point $B$

If $B=(x_B,y_B)$, then $B'=(-x_B,-y_B)$.

Since we don't have the actual coordinates of $R$, $Y$, and $B$ given in the grid, we just state the general rule - based transformation.

Answer:

If the coordinates of $R$ are $(x_R,y_R)$, $R'$ has coordinates $(-x_R,-y_R)$; if the coordinates of $Y$ are $(x_Y,y_Y)$, $Y'$ has coordinates $(-x_Y,-y_Y)$; if the coordinates of $B$ are $(x_B,y_B)$, $B'$ has coordinates $(-x_B,-y_B)$.