Four checks for an exact location
A point has no length, width, or thickness. That can feel strange because the dot on a worksheet clearly takes up space. The dot has to be visible so our eyes can find it, but its visible size is not part of the geometry. If a teacher draws a larger dot or a smaller dot, the point has not become bigger or smaller. It is still one exact place. This is similar to placing a pin on a map: the pin helps you notice the location, but the location itself is not the size of the pin.
Points are the small building blocks used to make larger figures. The two ends of a line segment are points. The corner where two sides meet is a point called a vertex. The center of a circle is a point, and the place where two lines cross is an intersection point. When you learn the names of bigger shapes, you are often learning how several points are arranged and connected.
Points are also important on a coordinate plane. A coordinate pair such as (3, 2) gives directions to one exact place: move three units across and two units up. The first number tells the horizontal movement, and the second number tells the vertical movement. If you switch the numbers and plot (2, 3), you usually land somewhere else. The point has changed because its location has changed.
You can find points outside a mathematics book too. A chess piece sitting on a particular square has a location. A seat in a classroom can be named by its row and number. A spot on a treasure map can be described with directions. Geometry takes this everyday idea of location and makes it exact enough to name, plot, compare, and use in careful reasoning.
- A point names one exact location.
- The dot used to show a point is only a visible symbol; it does not have mathematical size.
- Capital letters such as A, B, and P are common names for points.
- A point can be an endpoint, a vertex, a center, or an intersection.
- One ordered pair identifies one location on a coordinate plane.