Question

consider quadrilateral wxyz plotted on the grid below. perform the following sequence of transformations and then give the coordinates of w, x, y and z. rotate quadrilateral wxyz about the origin 180°. translate the resulting figure 8 units to the right. note: do not use any spaces in your answer. the coordinates of w are: the coordinates of x are: the coordinates of y are: the coordinates of z are:

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 180° about the origin is $(x,y)\to(-x,-y)$.

Step2: Recall translation rule

The rule for translating a point $(x,y)$ 8 units to the right is $(x,y)\to(x + 8,y)$.

Step3: Assume initial coordinates

Let's assume the coordinates of $W=(2,2)$, $X=(4,6)$, $Y=(6,2)$, $Z=(4,0)$ from the grid (approximate values based on visual - inspection).

Step4: Perform rotation

For $W(2,2)$ after 180° rotation about the origin, $W_1=(-2,-2)$. After translation 8 units to the right, $W'=(-2 + 8,-2)=(6,-2)$.
For $X(4,6)$ after 180° rotation about the origin, $X_1=(-4,-6)$. After translation 8 units to the right, $X'=(-4 + 8,-6)=(4,-6)$.
For $Y(6,2)$ after 180° rotation about the origin, $Y_1=(-6,-2)$. After translation 8 units to the right, $Y'=(-6+8,-2)=(2,-2)$.
For $Z(4,0)$ after 180° rotation about the origin, $Z_1=(-4,0)$. After translation 8 units to the right, $Z'=(-4 + 8,0)=(4,0)$.

Answer:

The coordinates of $W'$ are:$(6,-2)$
The coordinates of $X'$ are:$(4,-6)$
The coordinates of $Y'$ are:$(2,-2)$
The coordinates of $Z'$ are:$(4,0)$