Examples of Math Problems: If the lines 4x-y+2=0 and x+2ky+1=0 are perpendicular to each other, determine the value of k

Friday, January 2, 2015

If the lines 4x-y+2=0 and x+2ky+1=0 are perpendicular to each other, determine the value of k

For a line in the general form,
Ax%2BBy%2BC=0

Ax%2BBy%2BC=0

,

m=-A%2FB

so

m%5B1%5D=-4%2F%28-1%29=4

and

m%5B2%5D=-1%2F%282k%29

we require that
m%5B1%5Dm%5B2%5D=-1

m%5B1%5Dm%5B2%5D=-1

therefore...
-4%2F%282k%29=-1

-4%2F%282k%29=-1

so

k=2

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