Finding co-ordinates in squares

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Homework Help Overview

The problem involves finding the coordinates of vertices B and D of a square ABCD, given two vertices A(7,2) and C(1,4), and the equation of diagonal BD as y=3x-9. The original poster expresses confusion about how to determine the coordinates despite having calculated the midpoints and the equation of the diagonal.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the slopes of the diagonals, with one suggesting that the product of the slopes should equal -1. Others mention the properties of the midpoints and distances in relation to the square's geometry.

Discussion Status

The discussion is ongoing, with some participants offering insights into the geometric properties of squares and diagonals. The original poster appears to gain clarity from the contributions, indicating a potential shift towards understanding.

Contextual Notes

The original poster mentions difficulty in visualizing the problem through graphing, which may affect their ability to interpret the relationships between the points and lines involved.

bob4000
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urgent! finding co-ordinates in squares

A(7,2) and C(1,4) are vertices of a square ABCD.

equation BD is y=3x-9

midpoints AC: (4,3)

find the co-ordinates of B and D

i just don't understan how to get the co-ordinates, I've tried plotting a graph but to no avail. i found the midpoints and the equation listed above with relative ease but this part of the question just baffles me. if anyone could just explain the method of this kind of task, i will be able to answer the question. thank you.
 
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It might help to use the fact that the product of the slopes of the diagonals is -1.
 
i used tht to find the equation, but i don't see how that can help me with the co-ordinates?
 
It's even easier than I thought. The diagonals have the same midpoint and the distances from the midpoint to each corner are all the same.
 
i think i get it now. thanks a lot
 

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