The problem shown in the image asks to rotate triangle $\triangle PQR$ by 270° counterclockwise around the origin. Let's break down how to approach this type of transformation:

1. Rotation of points 270° counterclockwise:

   • The general rule for a 270° counterclockwise rotation around the origin is to switch the coordinates of each point and negate the new first coordinate.
   • For a point $(x, y)$, the transformation is: $(x, y) \rightarrow (y, -x)$

2. Applying the rule to each vertex of the triangle:

   • Assume the coordinates of $P$, $Q$, and $R$ are $P(x_1, y_1)$, $Q(x_2, y_2)$, and $R(x_3, y_3)$. Based on the diagram, these points will be rotated using the rule $(x, y) \rightarrow (y, -x)$.
   • After the transformation, the new coordinates of $P'$, $Q'$, and $R'$ will be plotted on the graph.

Would you like me to calculate the new coordinates of the points $P$, $Q$, and $R$ from the diagram? Let me know if you need more details on any specific part of the process!

Further Questions to Explore:

1. What is the rule for a 90° counterclockwise rotation around the origin?
2. How does the rotation affect the orientation of the shape?
3. What happens to a shape's size and angles during rotation?
4. How can you verify the accuracy of a transformation on a graph?
5. How does the triangle's image differ after a reflection instead of a rotation?

Tip: Always remember the origin is the fixed point during any rotation unless stated otherwise.