Finding the Equation of a Perpendicular Line Passing Through Two Points

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SUMMARY

The discussion focuses on finding the equation of a line perpendicular to line AB, which passes through points A (3,4) and B (7,-6). The gradient of line AB is calculated as -2.5. To find the gradient of the perpendicular line S, the relationship between the slopes of perpendicular lines is utilized, where the product of their slopes equals -1. Consequently, the gradient of line S is determined to be +2.5.

PREREQUISITES
  • Understanding of coordinate geometry
  • Knowledge of slope calculations
  • Familiarity with the concept of perpendicular lines
  • Ability to manipulate linear equations
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  • Learn how to derive the equation of a line from a point and a slope
  • Study the concept of slope-intercept form and standard form of linear equations
  • Explore the relationship between slopes of parallel and perpendicular lines
  • Practice solving problems involving equations of lines in coordinate geometry
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equation of a line problem!

The points A and B have co-ordinates (3,4) and (7,-6) respectively. the straight line S passes through A and is perpendicular to AB.
FInd an equation for S, giving your answer in the form ax+by+c=0

Ok so I am really stuck on this question. So far i have calculated the gradient of the line AB by doing (-6-4)/(7-3) and i got -2.5

But now i don't know what to do please help :rolleyes:
 
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How are the slopes of perpendicular lines related?
 
i have no idea how the slopes are related
 
Two lines with gradients m and m' are perpendicular if (m)(m')=-1
 
so would that mean that my gradient is +2.5
 
Would it?

If m' x (-2.5) = -1, what does m' = ?
 

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