+0

# Help. ​

0
115
1
+492

Help.

NotTheSmartest  Mar 7, 2017
Sort:

#1
+82801
0

We can prove this as follows :

Connect all four midpoints

Distance from    (-a, b) to (a,b)   =  2a

Distance from    (-a, -b) to (a, - b) =  2a ....so  these  opposite sides are congruent

Distance from (-a, b) to (-a, -b)  = 2b

Distance from (a,b) to ( a, -b) = 2b......so these opposite sides are congruent

And the slope between (-a,b) and (a,b)  =   [b - b] / [-a - a]  =  0

And the slope between (-a,-b) and (a, -b)  = [ - b - -b] / [ -a -a] =  0.....so.....these opposite sides are parallel

And the slope between (-a,b) and (-a, -b)  = [-b - b] / [ -a - - a] =  is undefined

And the slope between (a,b) and (a,-b) = [-b - b] / [a - a]  is undefined....so these opposite sides are parallel

And the diagonals drawn from (-a,b) to (a, -b)  and from (-a,-b) to (a,b)  meet at the origin and they bisect each other since the distance from the origin to each of these points = sqrt(a^2 + b^2)

So...the opposite sides are congruent and parallel  and the diagonals bisect each other.....thus.....this is a rectangle

CPhill  Mar 7, 2017

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details