Question

1. if parallelogram defg was rotated about the origin 180° counter - clockwise to create parallelogram defg, what are the vertex coordinates of image defg? enter the vertex coordinates in the boxes below.

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180° counter - clockwise about the origin, the new coordinates are $(-x,-y)$.

Step2: Identify original coordinates

Assume the original coordinates of the vertices of parallelogram $DEFG$ are $D(x_1,y_1)$, $E(x_2,y_2)$, $F(x_3,y_3)$, $G(x_4,y_4)$.

Step3: Apply rotation rule

The new coordinates of $D'$ are $(-x_1,-y_1)$, of $E'$ are $(-x_2,-y_2)$, of $F'$ are $(-x_3,-y_3)$ and of $G'$ are $(-x_4,-y_4)$. You need to first identify the original coordinates of the vertices from the graph and then apply the above - mentioned transformation to get the new coordinates.

Since the original vertex coordinates are not given in the text (only the graph is shown and we can't read them precisely from the text - based description), if we assume the original coordinates of the vertices of parallelogram $DEFG$ are $D(-2,4)$, $E(-1,2)$, $F(-3,1)$, $G(-4,3)$:
For point $D(-2,4)$: After 180° counter - clockwise rotation about the origin, $D'=(2,-4)$.
For point $E(-1,2)$: After 180° counter - clockwise rotation about the origin, $E'=(1,-2)$.
For point $F(-3,1)$: After 180° counter - clockwise rotation about the origin, $F'=(3,-1)$.
For point $G(-4,3)$: After 180° counter - clockwise rotation about the origin, $G'=(4,-3)$.

Answer:

The vertex coordinates depend on the original coordinates. If the original coordinates of $D$, $E$, $F$, $G$ are $(-2,4)$, $(-1,2)$, $(-3,1)$, $(-4,3)$ respectively, then the new coordinates of $D'$, $E'$, $F'$, $G'$ are $(2,-4)$, $(1,-2)$, $(3,-1)$, $(4,-3)$ respectively.