Question

Quadrilateral A′B′C′D′ is obtained by a reflection across the y-axis of quadrilateral ABCD, followed by a translation 3 units to the left and 3 units down. Create a function modeling the reflection and the translations. f(x, y) = (, )

Answer 1

Let's solve this problem step by step.

FIRST. Quadrilateral A′B′C′D′ is obtained by a reflection across the y-axis of quadrilateral ABCD

When we reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate changes in sign. So:

(x, y) → (-x, y)

SECOND. Followed by a translation 3 units to the left and 3 units down.

To translate a point 3 units to the left subtract 3 from the x-coordinate and to translate a point 3 units down subtract 3 from the y-coordinate. Therefore, the function we are looking for is:

f(x, y) = (-x - 3, y - 3)