Coordinate Perimeter

Coordinate Perimeter

When a shape is drawn on a coordinate grid, its perimeter is the total distance around the outside. The key idea is to find the length of each side from the coordinates, then add those lengths.

1) Find each side length

For horizontal or vertical sides, count the number of grid units between the endpoints. If a side is not horizontal or vertical, use the distance between the two points. For points ((x_1,y_1)) and ((x_2,y_2)), the distance is found from the changes in x and y.

2) Add all side lengths

List every side once and add them carefully. For polygons like rectangles, squares, triangles, or other coordinate figures, make sure no side is missed.

3) Simplify the result

Combine like terms, reduce fractions if needed, and write the perimeter in simplest form. If the answer involves radicals, leave them simplified.

4) Check your work

A good check is to see whether the total perimeter is reasonable compared with the size of the figure on the grid. Also verify that each side length matches the coordinates and that all sides were included.

Helpful tip

If the figure has repeated side lengths, you may be able to use symmetry or equal sides to save time. Still, always confirm the final total by adding all boundary lengths.