Q 89 - Precalculus Enhanced with Graphing Utilities

Question

Open the x-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?

Step-by-Step Solution

Answer

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

Step 1. Given information

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

Step 2. Relation between coordinates

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

Step 3

The conclusion is the same if we move point A along the other quadrant

If $A(x, y)$ then $B(x,-y)$