Question

Open the y-axis symmetry applet. Move point A around the Cartesian plane with your mouse. How are the coordinates of point A and the coordinates of point B related?

Short answer

Point B which is axisymmetric to point A(x, y) with respect to the y axis has coordinates$B\left(-x,y\right)$

Step-by-step solution

Step 1. Given Information

Open the y-axis symmetry applet. Move point A around the Cartesian plane with your mouse.

Step 2. Relation between coordinates

If point A moves away from the y-axis then point B will also move away, because the distance between point B and point A to the y-axis are equal.

Step 3. 

In the above case, the y-coordinates of point A and point B are equal, but the x-coordinate of the points are opposite.

If$A\left(x,y\right)$then$B\left(-x,y\right)$