When a segment is rotated 270^(∘) 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 XY, we can find the endpoints of X'Y'.
Point
(a,b)
(b,- a)
X
(-3,1)
(1,3)
Y
(4,- 5)
(- 5,- 4)
From the table, we can determine the coordinates of the image.
X'(1,3) and Y'(- 5, - 4)
Knowing the endpoints of X'Y', we can draw the image.
Reflection
To reflect X'Y', across the y-axis, we will move the vertices of this figure to the opposite side of the axis while maintaining the distance of each point from the axis. Using this rule with the endpoints of X'Y', we can find the endpoints of X''Y''.
Point
(a,b)
(- a,b)
X'
(1,3)
(- 1,3)
Y'
(- 5,- 4)
(5,- 4)
Knowing the endpoints of X''Y'', we can draw the image.
Final Composed Image
The final composed image will be the final product of both transformations.
