Definition
Vertical
Vertical describes an up-and-down direction chosen for a diagram or coordinate system.
What it means
Imagine the direction from the bottom of the page toward the top. A vertical line follows that direction. Turning the page changes what looks vertical on the page, so vertical describes orientation rather than a special kind of shape.
Remember it
Vertical runs from bottom to top in the chosen view.
Example
On a standard coordinate plane, the points (3, 1), (3, 4), and (3, 7) lie on x = 3. Their x-coordinate stays 3, so the line through them is vertical.
Watch for
Vertical depends on the chosen view or coordinate system; it is not an unchanging property of an unlabelled line in space.
Common mix-up
Vertical and perpendicular are different. A vertical line can be perpendicular to a horizontal line, but not every perpendicular line is vertical.
Exact meaning
A line or direction is vertical relative to the chosen orientation when it runs in the up-and-down direction. On a standard coordinate plane, every vertical line has equation x = c, so its x-coordinate stays constant.