Question

If the point (6,3) was reflected across the line x=2 and then it’s image was reflected across the x axis what translation would be needed to move this second image back to where the point started

Answer 1

right 4 units

Explanation:

The reflection across x=2 makes the transformation ...

(x, y) ⇒ (4 -x, y)

The reflection across x=0 makes the transformation ...

(x, y) ⇒ (-x, y)

The two transformations together make the transformation ...

(x, y) ⇒ (-(4-x), y) = (x -4, y)

To get the original point back, we need the translation ...

(x, y) ⇒ (x +4, y) . . . . . translate right 4 units

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Check

That, together with the original pair of reflections gives ...

(x, y) ⇒ ((x -4) +4, y) = (x, y) . . . the original point