Question

the shape above has the following coordinates: r (0,0), y (6,3), g (9,8) and b (1,10) rotate the shape 180° counterclockwise. what are the coordinates of the image? r: y: g: b: then translate it 5 units right and 3 units up. what are the coordinates of the new image? r: y: g: b

Explanation:

Step1: Apply 180 - degree counter - clockwise rotation rule

The rule for a 180 - degree counter - clockwise rotation about the origin is $(x,y)\to(-x,-y)$.
For point $R(0,0)$: $R'=(0,0)$; for point $Y(6,3)$: $Y'=(-6,-3)$; for point $G(9,8)$: $G'=(-9,-8)$; for point $B(1,10)$: $B'=(-1,-10)$.

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 5,y+3)$.
For $R'(0,0)$: $R''=(0 + 5,0+3)=(5,3)$; for $Y'(-6,-3)$: $Y''=(-6 + 5,-3+3)=(-1,0)$; for $G'(-9,-8)$: $G''=(-9 + 5,-8+3)=(-4,-5)$; for $B'(-1,-10)$: $B''=(-1 + 5,-10+3)=(4,-7)$.

Answer:

$R'$: $(0,0)$
$Y'$: $(-6,-3)$
$G'$: $(-9,-8)$
$B'$: $(-1,-10)$
$R''$: $(5,3)$
$Y''$: $(-1,0)$
$G''$: $(-4,-5)$
$B''$: $(4,-7)$