Question

How can the Distance and Midpoint Formulas be used to identify specific polygons?

Answer 1

There is a way to prove that a quadrilateral is a rectangle.
If all angles in a quadrilateral are right angles, then it’s a rectangle (reverse of the rectangle definition). (Actually, you only need to show that three angles are right angles — if they are, the fourth one is automatically a right angle as well.)
you can also use the distance formula to find out

distance forumula= Square root of (X2-X1)^2+(Y2-Y1)^2

let' use A and B

for A 6 is X^2 Y^2 is 0

for B 3 is X^1 Y^1 is 9 (the order does matter)

well now plug it in!

(6-3)^2+(2-1)^2

(3)^2+(1)^2

9+1

so now it's square root of 10