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 rotation rule

When rotating a point (x,y) 180° counter - clockwise about the origin, the new coordinates (x',y') are given by (-x,-y).
For R(0,0): x = 0, y = 0, so R'=(-0,-0)=(0,0)
For Y(6,3): x = 6, y = 3, so Y'=(-6,-3)
For G(9,8): x = 9, y = 8, so G'=(-9,-8)
For B(1,10): x = 1, y = 10, so B'=(-1,-10)

Step2: Apply translation rule

The translation rule for moving a point (x,y) 5 units right and 3 units up is (x + 5,y + 3).
For R'(0,0): x = 0, y = 0, so R''=(0 + 5,0+3)=(5,3)
For Y'(-6,-3): x=-6, y=-3, so Y''=(-6 + 5,-3 + 3)=(-1,0)
For G'(-9,-8): x=-9, y=-8, so G''=(-9 + 5,-8 + 3)=(-4,-5)
For B'(-1,-10): x=-1, y=-10, so 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)