Question

How can the Distance and Midpoint Formulas be used to identify specfic polygons? For example, how could you show that a quadrilateral is a rectangle?

Answer 1

In analytical geometry, the distance formula is used to find the distance between lines, points, or between a line and a point. If you want to know what specific polygon the coordinates of the points makes, then you are going to use the distance formula for points. The equation is 

d = √[(x₂-x₁)²+(y₂-y₁)²]

where x₁ & y₁ and x₂ & y₂ are coordinates of points 1 and 2

Now, you have to draw the coordinates on the Cartesian plane first. Then, identify two adjacent points and find the distance using the given formula. Do this for all pair of adjacent points. If you get two sets of equal lengths, then that polygon is a rectangle. Because by definition, a rectangle is a quadrilateral having two pairs of parallel and equal side lengths.