Question

graph the image of △cde after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify vertices of $\triangle CDE$

Let's assume the coordinates of point $C$ are $(x_1,y_1)$, point $D$ are $(x_2,y_2)$ and point $E$ are $(x_3,y_3)$.

Step3: Apply rotation rule to each vertex

For point $C(x_1,y_1)$, the new coordinates $C'$ will be $(-y_1,x_1)$. For point $D(x_2,y_2)$, the new coordinates $D'$ will be $(-y_2,x_2)$. For point $E(x_3,y_3)$, the new coordinates $E'$ will be $(-y_3,x_3)$.

Step4: Plot new vertices

Plot the points $C'$, $D'$ and $E'$ on the coordinate plane and connect them to form the image of $\triangle CDE$ after the 90 - degree counter - clockwise rotation around the origin.

Since the actual coordinates of $C$, $D$ and $E$ are not given in the text (only the instruction and the grid are shown), we cannot give the exact numerical coordinates of the rotated points. But the general procedure for graphing the rotated triangle is as above.

Answer:

Step1: Recall rotation rule

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

Step2: Identify vertices of $\triangle CDE$

Let's assume the coordinates of point $C$ are $(x_1,y_1)$, point $D$ are $(x_2,y_2)$ and point $E$ are $(x_3,y_3)$.

Step3: Apply rotation rule to each vertex

For point $C(x_1,y_1)$, the new coordinates $C'$ will be $(-y_1,x_1)$. For point $D(x_2,y_2)$, the new coordinates $D'$ will be $(-y_2,x_2)$. For point $E(x_3,y_3)$, the new coordinates $E'$ will be $(-y_3,x_3)$.

Step4: Plot new vertices

Plot the points $C'$, $D'$ and $E'$ on the coordinate plane and connect them to form the image of $\triangle CDE$ after the 90 - degree counter - clockwise rotation around the origin.

Since the actual coordinates of $C$, $D$ and $E$ are not given in the text (only the instruction and the grid are shown), we cannot give the exact numerical coordinates of the rotated points. But the general procedure for graphing the rotated triangle is as above.