SOLUTION: Find the value of K to the right (K-2)x - (K-1)y - 7 = 0 is perpendicular to 2x - 7y +5 = 0 Thanks

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Question 547181: Find the value of K to the right (K-2)x - (K-1)y - 7 = 0 is perpendicular to 2x - 7y +5 = 0
Thanks
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If two lines are perpendicular, the product of their slopes is -1. And if the product of the slopes of two lines is -1, the lines are perpendicular.
Solving the two equations for y, I get:
%28K-2%29x+-+%28K-1%29y+-+7+=+0-->%28K-2%29x+-+7+=%28K-1%29y+-->y=%28K-2%29x%2F%28K-1%29+-+7+%2F%28K-1%29 with slope=%28K-2%29%2F%28K-1%29
2x+-+7y+%2B5+=+0-->2x+%2B5+=+7y-->y=%282%2F7%29x+%2B5%2F7 with slope=2%2F7
For the two lines to be perpendicular, it has to be:
%28%28K-2%29%2F%28K-1%29%29%282%2F7%29=-1-->%28K-2%29%282%2F7%29=-%28K-1%29-->2%28K-2%29=-7%28K-1%29%29-->2%28K-2%29%2B7%28K-1%29=0-->2K-4%2B7K-7=0-->9K-11=0-->9K=11-->K=11%2F9