Question

rotate triangle def 90° counterclockwise around the center f. plot point e.

Explanation:

Step1: Recall rotation rule

For a 90 - degree counter - clockwise rotation around a point $(a,b)$ of a point $(x,y)$, the new point $(x',y')$ is given by the transformation $(x - a,y - b)\to-(y - b,x - a)$ and then $(x',y')=(a-(y - b),b+(x - a))$. In a grid - based system, we can also use geometric understanding. If we consider the vector from the center of rotation $F$ to point $E$, for a 90 - degree counter - clockwise rotation, we swap the $x$ and $y$ displacements from the center of rotation and change the sign of one of them.

Step2: Analyze grid displacements

Count the horizontal and vertical displacements of point $E$ from point $F$. Let's assume $F$ is the origin of our local coordinate system for the rotation. If we count the grid units, we can find the new position of $E$. Suppose the horizontal displacement of $E$ from $F$ is $x_{EF}$ and the vertical displacement is $y_{EF}$. After a 90 - degree counter - clockwise rotation, the new horizontal displacement $x'_{EF}=-y_{EF}$ and the new vertical displacement $y'_{EF}=x_{EF}$.

Step3: Locate the new point

Based on the grid and the rotation rule, we can plot the new point $E'$.

Answer:

(Please note that without specific grid coordinates for $E$ and $F$, we can't give exact numerical coordinates for $E'$. But the general method to plot it is as described above. If we assume $F$ is at $(x_F,y_F)$ and $E$ is at $(x_E,y_E)$, then $E'$ is at $(x_F-(y_E - y_F),y_F+(x_E - x_F))$)