ADVERTISEMENT

Vertical line (Coordinate Geometry)
Try this
Drag the points A or B and note the line is vertical when they both have the same
x coordinate.
A vertical line is one the goes straight up and down,
parallel to the yaxis of the coordinate plane. All
points on the line will have the same xcoordinate.
In the figure above, drag either point and note that the line is vertical when they both have the same xcoordinate.
A vertical line has no
slope. Or put another way, for a vertical line the slope is undefined. As you
drag the points above, notice that the slope indicator goes away when the line is exactly vertical.
The equation of a vertical line is
x = a

Where:
x 
is the coordinate of any point on the line 
a 
is where the line crosses the xaxis (x intercept).


Notice that the equation is independent of y. Any point on the vertical line satisfies the equation.
Examples
Fig 1. Is the line vertical?
Determine if the line shown in Fig 1 is vertical and write its equation.
The points A and B on the line are at (15,3) and (15,20).
The first coordinate in each pair is the xcoordinate which are 15, and 15.
Since they are equal, the line is vertical.
Since the line crosses the xaxis at 15, the equation of the line is
x = 15;
which can be read as "for all values of y, x is 15".
Things to try

In the figure at the top of the page, drag the points around and note how points on vertical lines can have any ycoordinate,
but the xcoordinates are the same.

Click "hide details". Adjust the points to create a new vertical line. Write down the equation of the line
and then click "show details" to verify your answer.
Limitations
In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place.
This can cause calculatioons to be slightly off.
For more see
Teaching Notes
Other Coordinate Geometry entries
(C) 2009 Copyright Math Open Reference. All rights reserved

COMMON CORE
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out
