Answer:
rectangle, square, triangle
Explanation:
Given the coordinates of the vertices of a rectangle, triangle, and square, you want to sort them in order of increasing perimeter.
Side lengths
In general, the length of a side can be found using the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
This shows you that if the x-coordinates are the same, the distance is the positive difference of the y-coordinates, and vice versa.
The attachment shows the side lengths for the figures, computed using this formula. Each row shows the distance from the point on that row to the point on the next row. (You will notice the last point is a copy of the first point.)
Perimeter
The perimeter of each figure is the sum of the side lengths. This is the number below the Distance column in each of the tables.
In increasing order, the perimeters are ...
- Rectangle: 10
- Square: 12
- Triangle: ~19.06
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Additional comment
When the computations are repetitive, it is often convenient to let a spreadsheet do them. The formula can be entered once and copied where needed. The problem then reduces to one of data entry, which you generally have to do for any but mental arithmetic.