∆XYZ is rotated 180⁰ around the origin and translated 2 units down to produce ∆X'Y'Z'.
What is transformation of shape?
Given the pre-image vertices X(6,-2), Y(7,-6) and Z(1,-6) and image vertices of XYZ as X'(-6,0), Y'(-7,4) and Z'(-1,4)
When ∆XYZ is rotated 180⁰ around the origin
The coordinates of x and y are negated
new coordinates
X(6,-2) = (-6,2)
Y(7,-6) = (-7,6)
Z(1,-6) = (-1,6)
Translate the the new coordinates 2 units down.
(x,y) = (x,y-2)
X(-6,2) = X'(-6,0)
Y(-7,6) = Y'(-7, 4)
Z (-1,6) = Z'(-1,4)
This corresponds to vertices of the image.
Therefore, ∆XYZ is rotated 180⁰ around the origin and translated 2 units down to produce ∆X'Y'Z'.