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A is the point (8,3) and B is the point (12, 1).

Find the equation of the line, perpendicular to the line AB, which passes through the point (0,0).

Sagot :

Answer:

y = 2x

Step-by-step explanation:

calculate the slope of AB using the slope formula

m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (8, 3) and (x₂, y₂ ) = B (12, 1 )

[tex]m_{AB}[/tex] = [tex]\frac{1-3}{12-8}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2

the equation of a line passing through the origin (0, 0 ) is

y = mx

here m = 2 , then

y = 2x ← equation of perpendicular line

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