Prove: If the product of the slopes of two lines is -1, then the lines are perpendicular.

I have already proven the converse of this statement. I have no idea where to go / what to do for this proof...

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- Nov 15th 2010, 01:47 PMthamathkid1729Coordinate Proof... Perpendicular Lines
__Prove__: If the product of the slopes of two lines is -1, then the lines are perpendicular.

I have already proven the converse of this statement. I have no idea where to go / what to do for this proof... - Nov 16th 2010, 01:07 AMsa-ri-ga-ma
If θ1 and θ2 are the angles made by the two straight lines with x-axis, then the angle between the two straight line is given by

θ= θ2 - θ1.

Τhen tanθ = tan(θ2 - θ1) = (tanθ2 - tanθ1)/( 1 +tanθ1*tanθ2) = (m2 - m1)/(1 + m1*m2)

If m1*m2 = -1, tanθ becomes infiifnty which is possible when θ = π/2.