-gre.ge.11 x,y of fourth corner of diagonal

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Discussion Overview

The discussion revolves around identifying the fourth vertex of a rectangle given three vertices in the standard (x,y) coordinate plane. Participants explore the geometric relationships and calculations involved in determining this vertex.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant calculates the fourth corner as (3,-7) based on the deltas of the known vertices.
  • Another participant confirms the fourth vertex by considering the delta from one vertex to another and applying it to a different point.
  • A third participant notes that the lines connecting the given points are not perpendicular, suggesting that the line from one vertex to another is a diagonal of the rectangle.
  • A later reply acknowledges the observation that the configuration appears to form a rectangle.

Areas of Agreement / Disagreement

Participants generally agree on the identification of the fourth vertex as (3,-7), but there is no consensus on the necessity of additional calculations or the nature of the lines connecting the points.

Contextual Notes

Some assumptions about the rectangle's properties and the relationships between the vertices are not explicitly stated, leaving room for interpretation regarding the geometric configuration.

karush
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In the standard (x,y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

boyce_20201004144618.png

sorry about the huge image but couldn't find where to scale it down
a. (3,-7)
b. (4,-8)
c. (5,-1)
d. (8,-3)
e. (9,-3)

ok I don't think we need a bunch of equations to do this
$\delta$ x of the with is 3
$\delta$ y of the width is 2

so the fourth corner is
(6-3,-5-2)=(3,-7)
 
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I get that from (2, 1) to (6, -5) is a "delta" of (6- 2, -5- 1)= (4, -6). So the line parallel to that through (-1, -1) goes through (-1+ 4, -1- 6)= (3, -7) also.
 
Just to cover all bases I'd first show that the lines (-1, -1) to (6, -5) and (2, 1) to (-1, -1) are not perpendicular so the line from (-1, -1) to (6, -5) must be a diagonal.

-Dan
 
good point
by observation it sure looks like a rectangle
 

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