If a point (a,b) is reflected in the line y=x, then its image is the point (b,a).
Point
(a,b)
(b,a)
X
(- 3,1)
(1,- 3)
Y
(4,- 5)
(- 5,4)
When we know the endpoints of X'Y' we can graph this image.
Next we have to do a rotation of 180^(∘) about the origin. When a figure is rotated 180^(∘) counterclockwise about the origin, the coordinates of the image's endpoints will change in the following way.
(a,b)→ (- a,- b)
Using this rule on the endpoints of XY, we can find the endpoints of X'Y',
Point
(a,b)
(- a,- b)
X'
(1,- 3)
(- 1,3)
Y'
(- 5,4)
(5,- 4)
Now we can graph X''Y''.
Finally, we will remove all unnecessary parts of the graph.
