Question

graph the image of △lmn 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: Assume coordinates of vertices

Let's assume the coordinates of vertices of $\triangle LMN$ are $L(x_1,y_1)$, $M(x_2,y_2)$ and $N(x_3,y_3)$.

Step3: Apply rotation rule to $L$

The new coordinates of $L$ after rotation, $L'( - y_1,x_1)$.

Step4: Apply rotation rule to $M$

The new coordinates of $M$ after rotation, $M'( - y_2,x_2)$.

Step5: Apply rotation rule to $N$

The new coordinates of $N$ after rotation, $N'( - y_3,x_3)$.

Step6: Plot new triangle

Plot the points $L'$, $M'$ and $N'$ on the coordinate - plane and connect them to form the rotated triangle $\triangle L'M'N'$.

Answer:

Plot the new triangle $\triangle L'M'N'$ with vertices obtained by applying the $(x,y)\to(-y,x)$ rule to the vertices of $\triangle LMN$.