Question

Prove that the quadrilateral with vertices (2,5) (4,8) (7,6) and (5,3) is a rectangel

Answer 1

Answer: Line slopes:

m1= 3/2 defined by points (5,3) and (7,6)

m2= -2/3 defined by points (7,6) and (4,8)

m3 = 3/2 defined by points (4,8) and (2,5)

m4 = -2/3 defined by points (2,5) and (5,3)

All comply the orthogonal slopes rule (90º)

Explanation:

As those 4 point define a polygon, to check is that polygon is a rectangle, you need to compare the slopes of the lines defined by the 4 points and check that accomplish the following rule:

m1 = -(1/m2). this shows that the slopes are intersected in 90º angle.