Coordinate Geometry: Find A & B on 5x-12y=6 & 3x-4y=-2

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SUMMARY

The discussion focuses on finding the coordinates of points A and B on the line defined by the equation 5x - 12y = 6, given that both points are 4 units away from the line 3x - 4y = -2. Point A is located on the same side of the line 3x - 4y = -2 as the origin, while point B is on the opposite side. The solution requires understanding the geometric relationship between the two lines and applying the distance formula for points from a line.

PREREQUISITES
  • Coordinate geometry principles
  • Understanding of linear equations
  • Distance formula from a point to a line
  • Concept of perpendicular distances in geometry
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  • Study the distance formula for a point to a line in coordinate geometry
  • Learn how to determine the side of a line a point lies on
  • Explore systems of linear equations and their graphical interpretations
  • Investigate the properties of perpendicular lines in coordinate systems
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Students studying coordinate geometry, mathematics educators, and anyone interested in solving geometric problems involving lines and distances in a Cartesian plane.

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Homework Statement



The points A and B are located on the line 5x-12y=6.The perpendicular distances of A and B respectively from the line 3x-4y=-2 are both 4 units. A lies on the same side of 3x-4y=-2 as the origin ,and B lies on the other side. Find the coordinates of A and B.

Homework Equations





The Attempt at a Solution



I do not understand what it means by the line in red. It has been previously stated both A and B lies on the same line so now how can they be on different sides relative to the origin?
 
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A and B lie on the first line, but on each side of the second line.
 

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