Question

graph the image of △pqr 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

Let's assume the coordinates of $P=(x_1,y_1)$, $Q=(x_2,y_2)$ and $R=(x_3,y_3)$ from the graph.

Step3: Apply rotation rule to $P$

If $P=(x_1,y_1)$, then $P'=(-y_1,x_1)$.

Step4: Apply rotation rule to $Q$

If $Q=(x_2,y_2)$, then $Q'=(-y_2,x_2)$.

Step5: Apply rotation rule to $R$

If $R=(x_3,y_3)$, then $R'=(-y_3,x_3)$.

Step6: Plot new points

Plot the points $P'$, $Q'$ and $R'$ on the coordinate plane to get the image of $\triangle PQR$ after 90 - degree counter - clockwise rotation around the origin.

Answer:

Plot the new points obtained by applying the $(x,y)\to(-y,x)$ rule to the vertices of $\triangle PQR$.