anonymous
  • anonymous
Each set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral. Use the ideas in this section to determine if the quadrilateral is a rectangle.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
{(2,-1),(-2,1),(-2,-1),(1,-3)}
anonymous
  • anonymous
It just requires a simple answer of yes or no?
Directrix
  • Directrix
That is correct but to determine "yes" or "no," some reason must be given for the answer. The first thing I would do is the plot the points on a sheet of paper.

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anonymous
  • anonymous
On a graph?
Directrix
  • Directrix
I'm using notebook paper.
Directrix
  • Directrix
(1,-3) throws off the idea that the sides of the quadrilateral may be horizontal or vertical.
anonymous
  • anonymous
Oh so the answer would be no?
Directrix
  • Directrix
Why do you say that? Just wondering.
anonymous
  • anonymous
I am not sure i am confused sorry lol.
Directrix
  • Directrix
You were making a decision on how the figure looks. There's no need to be sorry. That might have worked if the (1,-3) had not been one of the vertices. I think we will have to find the slopes of the lines determined by the points as sides of the quadrilateral and see if any adjacent sides of the quad have slopes that are negative reciprocals.
Directrix
  • Directrix
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Directrix
  • Directrix
You find the slope of segment AB and I'll do the same for segment BC. Post your slope here. So will I.
Directrix
  • Directrix
slope of segment BC =[ -1 - (-3)] / ( 2 - 1) = 2/1. Slope of segment AB = ?
Directrix
  • Directrix
There's an online slope calculator at the link: http://www.basic-mathematics.com/slope-calculator.html
anonymous
  • anonymous
Wait i messed up somewhere?
Directrix
  • Directrix
What did you get for the slope of AB?
Directrix
  • Directrix
Get 0 in the denominator?
anonymous
  • anonymous
I think so yes.
Directrix
  • Directrix
The reason we'ere doing slopes is that adjacent sides of a rectangle are perpendicular. And, we're trying to determine if the quad is a rectangle. So, we need the slopes. Crank out your slope for AB and let's knock out this problem. slope is change in y over change in x --> (y2 - y1)/(x2-x1). Look how I showed my work. You do the same. slope of segment BC =[ -1 - (-3)] / ( 2 - 1) = 2/1.
anonymous
  • anonymous
My work is the same as yours except i got 3/1 on last part somehow...
Directrix
  • Directrix
Why don't you show your work? Slope of AB = [1 - (-1)] / [ (-2) -2] = 2/-4 = -1/2.
Directrix
  • Directrix
Slope of AB * slope of BC = (-1/2) * (2/1) = -1. So, segment AB is perpendicular to segment BC.
Directrix
  • Directrix
You do the slope of CD and post your work here.
anonymous
  • anonymous
I got BC=-1-(-3)/(2/1)= 3/1
Directrix
  • Directrix
ERROR --> -1-(-3) = -1 + 3 = 2
Directrix
  • Directrix
You do the slope of CD and post your work here.
anonymous
  • anonymous
I found the answer was yes.

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