Question

Given the following coordinates complete the reflection transformation.​

Answer 1

For a general point (x, y), a reflection across the line x = a transforms the point into:

(a + (a - x), y) = (2a - x, y)

So if we first do a reflection across the line x = 1, the new point will be:

(2*1 - x, y) = (2 - x, y)

And if we now do a reflection across the line x = 3, the new point will be:

(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)

Now that we have the general formula we can solve the question.

For the point (-5, 2)

The generated point after the reflections is:

(4 + (-5), 2) = (-1, 2)

For the point (-1, 5)

The generated point after the reflections is:

(4 + (-1), 5) = (3, 5)

For the point (0, 3)

The generated point after the reflections is:

(4 +0, 3) = (4, 3)