Question

43 rotation 90° counterclockwise about the origin polygon

Explanation:

Step1: Recall rotation rule

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

Step2: Identify polygon vertices

Let's assume the vertices of the polygon are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, $D(x_4,y_4)$. From the graph, if $A(-1,3)$, $B(-2,3)$, $C(-3,0)$, $D(-2, - 2)$.

Step3: Apply rotation rule to each vertex

For $A(-1,3)$: $(-3,-1)$; for $B(-2,3)$: $(-3,-2)$; for $C(-3,0)$: $(0,-3)$; for $D(-2,-2)$: $(2,-2)$.

Answer:

The new vertices of the rotated polygon are found by applying the $(x,y)\to(-y,x)$ rule to each original vertex. The new polygon is formed by these new vertices.