Question

fill in the missing numbers to make each rotation true.
figure wxyz is rotated $90^{\circ}$ clockwise around the origin to form figure $wxyz$.
① $w(5, \underline{\quad\quad\quad})$
② $x(4, \underline{\quad\quad\quad})$
③ $y(\underline{\quad\quad\quad}, 6)$
④ $z(\underline{\quad\quad\quad}, \underline{\quad\quad\quad})$

figure wxyz is rotated $180^{\circ}$ clockwise around the origin to form figure $wxyz$.
⑤ $w(4, \underline{\quad\quad\quad})$
⑥ $x(1, \underline{\quad\quad\quad})$
⑦ $y(\underline{\quad\quad\quad}, -1)$
⑧ $z(\underline{\quad\quad\quad}, \underline{\quad\quad\quad})$
$w(-4,5)$
$x(-1,4)$
$y(-6,1)$
$x(-8,3)$

Explanation:

Step1: Recall 90° clockwise rotation rule

For a point $(x,y)$, 90° clockwise rotation around origin gives $(y, -x)$.

Step2: Recall 180° rotation rule

For a point $(x,y)$, 180° rotation around origin gives $(-x, -y)$.

Step3: Calculate $W'(5, \_)$

Original $W(-4,5)$. Apply 90° rule: $(-4,5) \to (5, 4)$

Step4: Calculate $X'(4, \_)$

Original $X(-1,4)$. Apply 90° rule: $(-1,4) \to (4, 1)$

Step5: Calculate $Y'(\_, 6)$

Original $Y(-6,1)$. Apply 90° rule: $(-6,1) \to (1, 6)$

Step6: Calculate $Z'(\_, \_)$

Original $Z(-8,3)$. Apply 90° rule: $(-8,3) \to (3, 8)$

Step7: Calculate $W''(4, \_)$

Original $W(-4,5)$. Apply 180° rule: $(-4,5) \to (4, -5)$

Step8: Calculate $X''(1, \_)$

Original $X(-1,4)$. Apply 180° rule: $(-1,4) \to (1, -4)$

Step9: Calculate $Y''(\_, -1)$

Original $Y(-6,1)$. Apply 180° rule: $(-6,1) \to (6, -1)$

Step10: Calculate $Z''(\_, \_)$

Original $Z(-8,3)$. Apply 180° rule: $(-8,3) \to (8, -3)$

Answer:

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