Finding Vertices of a Rhombus: Method and Rules | Homework Help

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Homework Help Overview

The discussion revolves around finding the coordinates of vertex B (p, q) of a rhombus ABCD, given the coordinates of vertices A(7, 0), C(1, 2), and D(2, -5). The original poster expresses confusion regarding the placement of point B after calculating its coordinates, questioning the rules for determining the vertices of a rhombus.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the properties of a rhombus and the implications of vertex placement. Some suggest that the original poster may have mispositioned point B in their diagram, affecting the validity of their findings. Others mention the importance of understanding the definition of a rhombus and its characteristics, such as equal side lengths and parallel sides.

Discussion Status

The discussion is ongoing, with participants providing insights into the properties of rhombuses and questioning the original poster's diagram. There is no explicit consensus on the correct placement of point B, and various interpretations of the problem are being explored.

Contextual Notes

Participants note that the original poster's calculated coordinates for B (p=6, q=7) do not align with their sketch, leading to further inquiry about the rules for determining vertices in a rhombus. The original poster's method involving midpoints is also mentioned, though its effectiveness is questioned.

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Homework Statement



A(7.0 ) , B(p,q) , C(1,2 ) and D (2.-5) are vertices of rhombus ABCD. determine p and q , i use the method of midpoint of AC and BD to find the ans, suprisingly , i gt the ans.. my question is , what rule to follow when it co mes to finding the vertices of rhombus? the ans is p=6 , q=7 BUT when i sketch it on diagram , it doesn't make sense. can someone help me on this

Homework Equations

The Attempt at a Solution

 

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A rhombus is a parallelogram with sides of the same length. A square is an example of a rhombus.

In your diagram, you placed the B point in the wrong place it should be higher and more to the right to make the sides parallel.

EDIT I must have fallen asleep whenI said it was a parallelogram with parallel sides duh...
 
Last edited:
desmond iking said:

Homework Statement



A(7.0 ) , B(p,q) , C(1,2 ) and D (2.-5) are vertices of rhombus ABCD. determine p and q ,i use the method of midpoint of AC and BD to find the ans, suprisingly , i gt the ans..my question is , what rule to follow when it co mes to finding the vertices of rhombus? the ans is p=6 , q=7BUT when i sketch it on diagram , it doesn't make sense. can someone help me on this

Homework Equations

The Attempt at a Solution


It helps here to know what the definition of a 'rhombus' is:

http://en.wikipedia.org/wiki/Rhombus

It's a quadrilateral with all four sides having the same length.
 
jedishrfu said:
A rhombus is a parallelogram with sides of the same length. A square is an example of a rhombus.

In your diagram, you placed the B point in the wrong place it should be higher and more to the right to make the sides parallel.

A square is a rather specialized example of a rhombus, when you specify a right-angled corner. But true. More useful here is the parallelogram status, because we already have the opposite sides (CD and DA) available to us, so we just need to apply those to get AB or BC (using the other one as a check).

In the diagram, B and D are both in the wrong quadrants, not just slightly shifted. C could do with better positioning too.
 
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desmond iking said:

Homework Statement



A(7.0 ) , B(p,q) , C(1,2 ) and D (2.-5) are vertices of rhombus ABCD. determine p and q ,i use the method of midpoint of AC and BD to find the ans, suprisingly , i gt the ans..my question is , what rule to follow when it co mes to finding the vertices of rhombus? the ans is p=6 , q=7BUT when i sketch it on diagram , it doesn't make sense. can someone help me on this

Homework Equations

The Attempt at a Solution

Usually the vertexes of a polygon are numbered in a way that B is next to A anticlockwise and so on. See picture.
As the sides of the rhombus are parallel the vector drawn from A to B is the same as the vector drown form D to C.
rhombus.JPG
 

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