Question

Open the origin 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

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

Step-by-step solution

Step 1. Given information

Open the origin symmetry applet. Move point A around the Cartesian plane with your mouse.

Step 2. Relation between the coordinates

If point A moves from the origin then point B also moves away because the distance of point B and point A to the origin are equal.

Step 3. 

The x and y coordinates of points A and B are opposite values, therefore the conclusion is the same if we move point A along the other quadrants

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