Q 90 - Precalculus Enhanced with Graphing Utilities

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?

Step-by-Step Solution

Answer

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

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 $B\left(-x,-y\right)$