Determine coordinates of reflection given equation

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SUMMARY

The discussion focuses on determining the coordinates of the reflection of point P (4, 8) across the line defined by the equation y = -3/2x + 14. To find the reflection, one must first derive the equation of the line perpendicular to the given line that passes through point P. This involves substituting the coordinates of point P into the perpendicular line's equation and utilizing geometric principles to calculate the intersection point, which is essential for finding the reflection coordinates.

PREREQUISITES
  • Understanding of linear equations and their slopes
  • Knowledge of perpendicular lines in coordinate geometry
  • Familiarity with the concept of reflection across a line
  • Ability to perform algebraic substitutions and solve equations
NEXT STEPS
  • Learn how to derive the equation of a line given two points
  • Study the properties of perpendicular lines in coordinate geometry
  • Explore the geometric interpretation of reflections across lines
  • Practice solving reflection problems using different points and lines
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in mastering coordinate transformations and reflections in algebra.

euro94
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Homework Statement


Find the coordinates of reflection of the point P (4,8) in the line y=-3/2 x + 14


Homework Equations



y= -3/2x + 14

The Attempt at a Solution


find a point on the line?
 
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Can you find the equation of the line through (4, 8), perpendicular to that line? Do you see why you want that?
 
would you have to sub in the point 4,8 in the equation and find the dot product?
 

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