If a point, (a,b), is reflected in the x-axis, then its image is the point (a,- b).
Practice makes perfect
Let's begin by drawing △ LMN.
When a figure is reflected in the x-axis, the coordinates of its vertices will change in the following way.
preimage (a,b)→ image (a,- b)
Using this rule on the vertices of △ LMN, we can find the coordinates of the reflected figure.
Point
(a,b)
(a,- b)
L
(1,6)
(1,- 6)
M
(- 2,4)
(- 2,- 4)
N
(3,2)
(3,- 2)
Now we can draw △ L'M'N'.
The second transformation is a rotation by 270^(∘) counterclockwise about the origin. There is also a rule for how the coordinates of the image will change.
preimage (a,b)→ image (b,- a)
Using this rule on the endpoints of △ L'M'N', we can find the vertices of △ L''M''N''.
Point
(a,b)
(b,- a)
L'
(1,- 6)
(- 6,- 1)
M'
(- 2,- 4)
(- 4,2)
N'
(3,- 2)
(- 2,- 3)
Now we can draw △ L''M''N''.
Finally, we will remove △ L'M'N' from the diagram.
