Prove Rectangle: Dot Product Help

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Homework Help Overview

The original poster attempts to prove that a quadrilateral with given vertices is a rectangle using the dot product, specifically by checking the orthogonality of adjacent sides.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss checking the dot product of vectors AB and BC, with suggestions to verify arithmetic and consider the negative of vectors. There is a request for the original poster to show their calculations for further clarification.

Discussion Status

The discussion is ongoing, with participants providing guidance on checking calculations and exploring the properties of the dot product. There is no explicit consensus yet, as the original poster is still working through the problem.

Contextual Notes

There is a mention of potential arithmetic errors and the importance of careful sign handling in vector subtraction, which may affect the outcome of the dot product calculations.

Hollysmoke
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-Use the dot product to prove that the quadrilateral with vertices A(-4,1) B(4,5) C(7,-1) and D(-1,-5) is a rectangle.

I tried find AB dot BC = 0, but I'm not getting 0. So I'm stumped. Can someone help me out? =/
 
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Just check your arithmetic.
 
Try BA dot BC
 
You are aware, are you not, that AB= -BA so that if AB dot BC= 0, so is BA dot BC?

Hollysmoke, could you show us what you got for AB and BC? I wondering if you were sufficiently careful of signs while subtracting.
 
HallsofIvy said:
You are aware, are you not, that AB= -BA so that if AB dot BC= 0, so is BA dot BC?

Hollysmoke, could you show us what you got for AB and BC? I wondering if you were sufficiently careful of signs while subtracting.

pfft, you are right. That's what I get for posting late at night. :rolleyes:
 

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