Question

the shape above has the following coordinates: r (0,2), y (10,4) and b (9,6) rotate the shape 270° clockwise. what are the coordinates of the image? r: y: b: then translate it 4 units right and 8 units down. what are the coordinates of the new image? r: y: b

Explanation:

Step1: Apply 270 - degree clockwise rotation rule

The rule for a 270 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$.
For point $R(0,2)$: $R'(2,0)$
For point $Y(10,4)$: $Y'(4,- 10)$
For point $B(9,6)$: $B'(6,-9)$

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 4,y - 8)$.
For $R'(2,0)$: $R''(2 + 4,0 - 8)=(6,-8)$
For $Y'(4,-10)$: $Y''(4 + 4,-10 - 8)=(8,-18)$
For $B'(6,-9)$: $B''(6+4,-9 - 8)=(10,-17)$

Answer:

$R'$: $(2,0)$
$Y'$: $(4,-10)$
$B'$: $(6,-9)$
$R''$: $(6,-8)$
$Y''$: $(8,-18)$
$B''$: $(10,-17)$