Question

lesson 2 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(__,__)
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 clockwise rotation rule

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

Step2: Find coordinates for 90 - degree clockwise rotation

1. For point $W$ (assume original coordinates $(x,y)$), after 90 - degree clockwise rotation, if $W'$ has $x$ - coordinate 5, from the rule, if the original $y = 5$ and original $x=-y'$, assume original $W(- 3,5)$ (by observing the graph), then $W'(5,3)$.
2. For $X$, assume original $X(-1,4)$, then $X'(4,1)$.
3. For $Y$, if $Y'(x,6)$, from the rule, original $Y(-6,y)$, assume original $Y(-6,1)$, then $Y'(-1,6)$.
4. For $Z$, assume original $Z(-5,2)$, then $Z'(2,5)$.

Step3: Recall 180 - degree clockwise rotation rule

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

Step4: Find coordinates for 180 - degree clockwise rotation

1. Assume original $W(-4, - 5)$, then $W'(4,5)$.
2. Assume original $X(-1,-4)$, then $X'(1,4)$.
3. Assume original $Y(-6,-1)$, then $Y'(6,-1)$.
4. Assume original $Z(-5,-2)$, then $Z'(5,2)$.

Step5: Recall 90 - degree counter - clockwise rotation rule

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

Step6: Find coordinates for 90 - degree counter - clockwise rotation

1. Assume original $W(-3,5)$, then $W'(-5,-3)$.
2. Assume original $X(-1,4)$, then $X'(-4,-1)$.
3. Assume original $Y(-6,1)$, then $Y'(-1,-6)$.
4. Assume original $Z(-5,2)$, then $Z'(-2,-5)$.

Answer:

1. $3$
2. $1$
3. $-1$
4. $2,5$
5. $5$
6. $4$
7. $6$
8. $5,2$
9. $-3$
10. $-4$
11. $-1,-6$
12. $-2,-5$