Question

r90 (x, y) → ( , ) r180° (x, y) → ( , ) r270° (x, y) → ( , ) examples perform the rotations. 1. r90° 2. r270° (2, 6) → ( , ) (15, -9) → ( , ) (-2, 0) → ( , ) (-6, -10) → ( , ) exercises perform the rotations. 3. r90° 4. r180° (16, 9) → ( , ) (-13, -54) → ( , ) (-51, 19) → ( , ) (17, -12) → ( , ) 5. r270° 6. r90° (-73, 9) → ( , ) (-13, 2) → ( , ) (8, 1) → ( , ) (10, 0) → ( , ) 7. r270° 8. r180° (0, 2) → ( , ) (10, -2) → ( , ) (10, 0) → ( , ) (-101, -42) → ( , )

Explanation:

Step1: Recall 90 - degree rotation rule

For a 90 - degree counter - clockwise rotation $R_{90^{\circ}}$, the rule is $(x,y)\to(-y,x)$.

Step2: Recall 180 - degree rotation rule

For a 180 - degree rotation $R_{180^{\circ}}$, the rule is $(x,y)\to(-x,-y)$.

Step3: Recall 270 - degree rotation rule

For a 270 - degree counter - clockwise rotation $R_{270^{\circ}}$, the rule is $(x,y)\to(y, - x)$.

Step4: Apply rules to examples

For $R_{90^{\circ}}$:

• $(2,6)\to(-6,2)$
• $(-2,0)\to(0, - 2)$
• $(16,9)\to(-9,16)$
• $(-51,19)\to(-19,-51)$
• $(-13,2)\to(-2,-13)$
• $(10,0)\to(0,10)$

For $R_{180^{\circ}}$:

• $(-13,-54)\to(13,54)$
• $(17,-12)\to(-17,12)$
• $(10,-2)\to(-10,2)$
• $(-101,-42)\to(101,42)$

For $R_{270^{\circ}}$:

• $(15,-9)\to(-9,-15)$
• $(-6,-10)\to(-10,6)$
• $(-73,9)\to(9,73)$
• $(8,1)\to(1,-8)$
• $(0,2)\to(2,0)$
• $(10,0)\to(0,-10)$

Answer:

1. $(-6,2)$; $(0, - 2)$
2. $(-9,-15)$; $(-10,6)$
3. $(-9,16)$; $(-19,-51)$
4. $(13,54)$; $(-17,12)$
5. $(9,73)$; $(1,-8)$
6. $(-2,-13)$; $(0,10)$
7. $(2,0)$; $(0,-10)$
8. $(-10,2)$; $(101,42)$