Points inside and outside a figure

A figure can be any closed shape or boundary, such as a square, circle, or polygon. When we talk about points inside or outside a figure, we are referring to points that are within or outside the boundaries of the given figure. Let's discuss the points inside and outside a figure in detail.

Points inside the figure:
Points that lie within the boundaries of the figure are considered to be inside the figure. These points are often referred to as interior points.

Points outside the figure:
Points that lie outside the boundaries of the figure are considered to be outside the figure. These points are often referred to as exterior points.

To determine whether a point is inside or outside a figure, we can use the following methods:

1. Visual inspection:
- Look at the given figure and identify its boundaries.
- If a point lies within the boundaries, it is inside the figure.
- If a point lies outside the boundaries, it is outside the figure.

2. Using coordinates:
- If we have the coordinates of the figure's boundaries and the point in question, we can use the concept of coordinate geometry to determine whether the point is inside or outside the figure.
- For example, if we have a square with vertices (0,0), (0,4), (4,4), and (4,0), and we want to determine whether the point (2,2) is inside or outside the square, we can compare the coordinates of the point with the boundaries of the square.
- In this case, the point (2,2) lies within the boundaries of the square and is therefore inside the figure.

In conclusion, points inside a figure are those that lie within the boundaries of the figure, while points outside a figure are those that lie outside the boundaries. We can determine whether a point is inside or outside a figure by visually inspecting the figure or by comparing the coordinates of the point with the boundaries of the figure using coordinate geometry.