Translations tell us how many units we should add to or subtract from the given coordinates. Let's look at the given translation.
(x,y) → (x,y + 2)
This means that we should move each endpoint of XY 2 units up.
From the diagram, we can determine the coordinates of the image.
X'(- 3,3) and Y'(4,- 3)
Rotation
When a segment is rotated 90^(∘) counterclockwise about the origin, the coordinates of the image's endpoints will change in the following way.
(a,b) → (- b,a)
Using this rule with the endpoints of X'Y', we can find the endpoints of X''Y''.
Point
(a,b)
(- b,a)
X'
(- 3,3)
(- 3,- 3)
Y'
(4,- 3)
(3,4)
Knowing the endpoints of X''Y'', we can draw the image.
Final Image
The final image X''Y'' will be the segment resulting from the translation followed by the rotation.
