Answer:
(-7, 5)
Step-by-step explanation:
You want to know the image of the point (-4, -6) after reflection in the x-axis and translation 3 left and 1 down.
Composition of transformations
The composition ...
[tex]T_{-3,-1}\circ r_{\text{x-axis}}[/tex]
is interpreted to mean reflection in the x-axis occurs first, then translation by (-3, -1).
That is, a composition of transformations is evaluated right to left.
Reflection
Reflection in the x-axis moves a point from below the x-axis to the same distance above the x-axis. That is, the sign of the y-coordinate changes:
(-4, -6) ⇒ (-4, 6) . . . reflection in the x-axis
Translation
The translation vector is added to the coordinates of the point:
(-4, 6) +(-3, -1) = (-4-3, 6-1) = (-7, 5)
The image of the point is located at (-7, 5).
