Question

figure wxyz is rotated 90° clockwise around the origin to form figure wxyz. 1. w(, ) 2. x(, ) 3. y(, 6) 4. z(, ) figure wxyz is rotated 180° clockwise around the origin to form figure wxyz. 5. w(4, ) 6. x(1, ) 7. y(, -1) 8. z(, ) figure wxyz is rotated 90° counter - clockwise around the origin to form figure wxyz. 9. w(-5, ) 10. x(, -1) 11. y(, ) 12. z(, )

Explanation:

Step1: Recall 90 - degree clock - wise rotation rule

The rule for a 90 - degree clock - wise rotation of a point $(x,y)$ around the origin is $(x,y)\to(y, - x)$.

Step2: Recall 180 - degree rotation rule

The rule for a 180 - degree rotation of a point $(x,y)$ around the origin is $(x,y)\to(-x,-y)$.

Step3: Recall 90 - degree counter - clockwise rotation rule

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

Assume the original coordinates of $W=(x_1,y_1)$, $X=(x_2,y_2)$, $Y=(x_3,y_3)$ and $Z=(x_4,y_4)$.

For 90 - degree clock - wise rotation:

1. If $W=(x_1,y_1)$, then $W'=(y_1,-x_1)$.
2. If $X=(x_2,y_2)$, then $X'=(y_2,-x_2)$.
3. If $Y=(x_3,y_3)$, then $Y'=(y_3,-x_3)$.
4. If $Z=(x_4,y_4)$, then $Z'=(y_4,-x_4)$.

For 180 - degree rotation:

1. If $W=(x_1,y_1)$, then $W'=(-x_1,-y_1)$.
2. If $X=(x_2,y_2)$, then $X'=(-x_2,-y_2)$.
3. If $Y=(x_3,y_3)$, then $Y'=(-x_3,-y_3)$.
4. If $Z=(x_4,y_4)$, then $Z'=(-x_4,-y_4)$.

For 90 - degree counter - clockwise rotation:

1. If $W=(x_1,y_1)$, then $W'=(-y_1,x_1)$.
2. If $X=(x_2,y_2)$, then $X'=(-y_2,x_2)$.
3. If $Y=(x_3,y_3)$, then $Y'=(-y_3,x_3)$.
4. If $Z=(x_4,y_4)$, then $Z'=(-y_4,x_4)$.

Since the original coordinates of the points $W$, $X$, $Y$ and $Z$ are not given in the problem statement, we cannot give specific numerical answers. But the general rules for rotation are as above.

If we assume we know the original coordinates of the points, for example, if $W=(a,b)$:

• For 90 - degree clock - wise rotation, $W'=(b,-a)$.
• For 180 - degree rotation, $W'=(-a,-b)$.
• For 90 - degree counter - clockwise rotation, $W'=(-b,a)$.

We need to see the original coordinates of the points $W$, $X$, $Y$ and $Z$ on the graph to calculate the exact new coordinates.

Since the original coordinates are not provided, we can only state the following:

1. For 90 - degree clock - wise rotation:

• The $x$ - coordinate of the new point is the $y$ - coordinate of the original point, and the $y$ - coordinate of the new point is the negative of the $x$ - coordinate of the original point.

1. For 180 - degree rotation:

• The $x$ - coordinate of the new point is the negative of the $x$ - coordinate of the original point, and the $y$ - coordinate of the new point is the negative of the $y$ - coordinate of the original point.

1. For 90 - degree counter - clockwise rotation:

• The $x$ - coordinate of the new point is the negative of the $y$ - coordinate of the original point, and the $y$ - coordinate of the new point is the $x$ - coordinate of the original point.

Answer:

Since the original coordinates of points $W$, $X$, $Y$ and $Z$ are not given, we cannot provide specific numerical answers for the coordinates of $W'$, $X'$, $Y'$ and $Z'$ after rotation. The general rotation rules are:

1. 90 - degree clock - wise rotation: $(x,y)\to(y, - x)$.
2. 180 - degree rotation: $(x,y)\to(-x,-y)$.
3. 90 - degree counter - clockwise rotation: $(x,y)\to(-y,x)$.