Prove Rectangle: Dot Product Help

In summary, the dot product can be used to prove that a quadrilateral is a rectangle by checking if the dot product of opposite sides is equal to 0. This was demonstrated through an example of finding the dot product of AB and BC, and then being reminded to be careful of signs when subtracting.
  • #1
Hollysmoke
185
0
-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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  • #2
Just check your arithmetic.
 
  • #3
Try BA dot BC
 
  • #4
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.
 
  • #5
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:
 

1. What is the definition of a rectangle?

A rectangle is a quadrilateral with four right angles and opposite sides that are equal in length.

2. How can the dot product be used to prove that a quadrilateral is a rectangle?

The dot product of two vectors is equal to the product of their magnitudes and the cosine of the angle between them. In the case of a rectangle, the angle between its adjacent sides is always 90 degrees, making the cosine of that angle equal to 0. Therefore, if the dot product of the two adjacent sides of a quadrilateral is 0, it can be proven that the quadrilateral is a rectangle.

3. Is the dot product the only way to prove a quadrilateral is a rectangle?

No, there are other methods such as using the Pythagorean theorem, congruent angles, or parallel sides to prove that a quadrilateral is a rectangle. However, the dot product is a commonly used method as it involves vectors and can be easily applied to different shapes and orientations.

4. Can the dot product be used to prove all types of quadrilaterals?

No, the dot product can only be used to prove that a quadrilateral is a rectangle. It cannot be used to prove other types of quadrilaterals such as squares, parallelograms, or rhombuses.

5. Are there any limitations to using the dot product to prove a rectangle?

Yes, the dot product can only be used to prove a rectangle if the quadrilateral has two adjacent sides that are perpendicular to each other. If this is not the case, then the dot product cannot be used to prove that the quadrilateral is a rectangle.

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