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This worksheet is about finding the equations of perpendicular lines.

 

Example Find the equation of the line perpendicular to
2x + 3y - 4 = 0 which goes through the point (0,-5).

 

Solution Rearrange 2x + 3y - 4 = 0 to make y the subject:
  y=
-2x
3
+
4
3
  The gradient of this line is
-2
3
(m in y=mx+c)
  The gradient of a line perpendicular to this is
3
2
.

 

The gradients of perpendicular lines have a product of -1

  ie. 
-2
3
×
3
2
= -1
  The gradient of this line is
-2
3
(compare y=mx+c)
  The gradient of a line perpendicular to this is
3
2
.

 

 

  The equation of the required line is y=
3
2
x - 5
or 2y - 3x + 10 = 0 after rearranging.

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