Question

the polygon below has a vertex marked with a large dot. draw the polygon after a rotation of 270° clockwise about the marked vertex.

Explanation:

Step1: Recall rotation rules

A 270 - degree clockwise rotation is equivalent to a 90 - degree counter - clockwise rotation. For a point $(x,y)$ rotated 90 degrees counter - clockwise about the origin $(0,0)$, the transformation rule is $(x,y)\to(-y,x)$. When rotating about a non - origin point $(a,b)$, we first translate the polygon so that the center of rotation $(a,b)$ becomes the origin, perform the rotation using the origin - centered rule, and then translate back.
Let the marked vertex be $(a,b)$. For each vertex $(x,y)$ of the polygon:

1. Translate: $(x_1,y_1)=(x - a,y - b)$
2. Rotate 90 degrees counter - clockwise: $(x_2,y_2)=(-y_1,x_1)$
3. Translate back: $(x_3,y_3)=(x_2 + a,y_2 + b)$

Step2: Apply to each vertex

Identify the coordinates of each vertex of the original polygon relative to the marked vertex (the center of rotation). Then apply the above three - step transformation process to each vertex.

Step3: Connect the new vertices

Once all the new vertices are found after the rotation and translation process, connect them in the same order as in the original polygon to draw the rotated polygon.

Since this is a drawing problem and we can't actually draw in this text - based format, the steps above describe how to perform the rotation geometrically.

Answer:

Follow the steps above to draw the rotated polygon on the given grid.