Question

What are the coordinates of point A (4,-1) after it has been reflected over the y-axis?

Answer 1

`(4,-1)` after reflection over the y-axis would become `color(red)(""(-4,-1))`

Explanation:

A reflection over the y-axis leaves the point the same distance above the x-axis (that is the y-coordinate value does not change).

The x-coordinate value becomes an equal distance from the y-axis but on the other side of the y-axis (that is the x-coordinate value becomes the negative of what it was).

Answer 2

`color(purple)(A ((4),(1)) to A'((-4), (-1))`

Explanation:

As can be seen from the above figure,

Mapping formula for reflection over y-axis is

`((x), (y)) to ((-x), (y))`

`:. color(purple)(A ((4),(-1)) to A'((-4), (-1))`