Finding the perpendicular of a line

 If we have the equation of a line, and want to find the equation of a line perpendicular to that, that passes through a certain point, we can derive it from the original equation!

The gradient of the perpendicular is the reciprocal of the original gradient!




To find the perpendicular, we need the gradient and a point it passes through to find the constant/ y-intercept.

So, let us take an equation:
y=2x+7

The gradient of the perpendicular would be the reciprocal of the gradient here, that is reciprocal of 2 which is -1/2!

Lets say that the perpendicular passes through the points (8,6)
Now we can find the complete equation:

6= -0.5(8) + c
Therefore, c = 10!

The equation of the perpendicular to y=2x+7 that passes through the point 8.6 is 
y=-0.5x + 10



Worked Examples:




Question:





Solution:
 m=-5
2= -40 +c
c=42
y=-5x+42

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