Question

Help pls i dont know how to do this

Answer 1

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 ...

  $T_{-3,-1}\circ r_{\text{x-axis}}$

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).