SOLUTION: Find the value of k so that the line containing the points (k,−7) and (6,6) is perpendicular to the line y=−2/7x+1.
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Question 720045: Find the value of k so that the line containing the points (k,−7) and (6,6) is perpendicular to the line y=−2/7x+1.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The slope of the line y = (2/7)x+1 is 2/7. The slope of any perpendicular line will be the negative reciprocal of the the slope of this line. So the slope of our perpendicular line will be -7/2.
The slope of the line through (k, -7) and (6, 6) will be (according to the slope formula):
or
We want the line through (k, -7) and (6, 6) to be perpendicular to y = (2/7)x+1. So its slope needs to be -7/2. Therefore:
Now we solve for k. Cross-multiplying we get:
Simplifying:
Adding 42:
Dividing by 7:
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