Question

3-3 additional practice
give the coordinates of each image. use a rule or graph paper to find your answer.

1. $r_{(90^circ, o)}(\triangle def)$ for $d(0,5), e(-2,8), f(-3,-5)$
2. $r_{(270^circ, o)}(wxyz)$ for $w(4,-2), x(7,3), y(1,11), z(-4,6)$
3. $r_{(180^circ, o)}(\triangle stu)$ for $s(-2,-6), t(-5,3), u(1,0)$
4. $r_{(360^circ, o)}(jklm)$ for $j(-4,7), k(1,5), l(6,1), m(3,-9)$

Explanation:

Step1: Recall rotation rules

Rotation rules about origin:

• $R_{90^\circ,O}(x,y)=(-y,x)$
• $R_{180^\circ,O}(x,y)=(-x,-y)$
• $R_{270^\circ,O}(x,y)=(y,-x)$
• $R_{360^\circ,O}(x,y)=(x,y)$

Step2: Solve Q1 ($R_{90^\circ,O}$)

$D(0,5)\to(-5,0)$; $E(-2,8)\to(-8,-2)$; $F(-3,-5)\to(5,-3)$

Step3: Solve Q2 ($R_{270^\circ,O}$)

$W(4,-2)\to(-2,-4)$; $X(7,3)\to(3,-7)$; $Y(1,11)\to(11,-1)$; $Z(-4,6)\to(6,4)$

Step4: Solve Q3 ($R_{180^\circ,O}$)

$S(-2,-6)\to(2,6)$; $T(-5,3)\to(5,-3)$; $U(1,0)\to(-1,0)$

Step5: Solve Q4 ($R_{360^\circ,O}$)

$J(-4,7)\to(-4,7)$; $K(1,5)\to(1,5)$; $L(6,1)\to(6,1)$; $M(3,-9)\to(3,-9)$

Answer:

1. $D'(-5,0)$, $E'(-8,-2)$, $F'(5,-3)$
2. $W'(-2,-4)$, $X'(3,-7)$, $Y'(11,-1)$, $Z'(6,4)$
3. $S'(2,6)$, $T'(5,-3)$, $U'(-1,0)$
4. $J'(-4,7)$, $K'(1,5)$, $L'(6,1)$, $M'(3,-9)$