Question

performing a rotation in the coordinate plane

fill in the missing numbers to make each rotation true.

figure wxyz is rotated 90° clockwise around the origin to form figure wxyz.
1 w(5,)
2 x(4,)
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(,)

Explanation:

Step1: Recall 90 - degree clockwise rotation rule

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

Step2: Find coordinates for 90 - degree rotation

1. Assume the original coordinates of $W$ are $(- 2,5)$. After a 90 - degree clockwise rotation, using the rule $(x,y)\to(y, - x)$, for $W(-2,5)$, $W'(5,2)$.
2. Assume the original coordinates of $X$ are $(- 4,4)$. After a 90 - degree clockwise rotation, $X'(4,4)$.
3. Assume the original coordinates of $Y$ are $(-6,1)$. After a 90 - degree clockwise rotation, $Y'(1,6)$.
4. Assume the original coordinates of $Z$ are $(-8,3)$. After a 90 - degree clockwise rotation, $Z'(3,8)$.

Step3: Recall 180 - degree rotation rule

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

Step4: Find coordinates for 180 - degree rotation

1. Assume the original coordinates of $W$ are $(- 2,5)$. After a 180 - degree rotation, $W'(2,-5)$.
2. Assume the original coordinates of $X$ are $(- 4,4)$. After a 180 - degree rotation, $X'(4,-4)$.
3. Assume the original coordinates of $Y$ are $(-6,1)$. After a 180 - degree rotation, $Y'(6,-1)$.
4. Assume the original coordinates of $Z$ are $(-8,3)$. After a 180 - degree rotation, $Z'(8,-3)$.

Answer:

1. $2$
2. $4$
3. $1$
4. $3,8$
5. $- 5$
6. $-4$
7. $6$
8. $8,-3$