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Question 1200253: Find the value of K so that the two lines are perpendicular. Line one contains the points (-6,4) and (-2,5) and line two contains the points (-3,4) and (0,k).
I know I need to do y2-y1/x2-x1 so I did that for both of them and got (1/4) for the first line and (k-4/3) for the second line.
Here is where I need help because I don't know what to do next. Any and all help is greatly appreciated :)
Found 2 solutions by htmentor, math_tutor2020:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Perpendicular lines have negative reciprocal slopes. You have correctly determined
that the slope of the line through (-6,4) and (-2,5) is 1/4. Thus, the line
through the points (-3,4) and (0,k) has a slope of -4.
-4 = (k-4)/(0-(-3)) -> (k-4)/3 = -4 -> k-4 = -12 -> k = -8.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Rule: Any two perpendicular lines, where neither is vertical nor horizontal, will have their slopes multiply to -1.
The slope through (-6,4) and (-2,5) is 1/4, which you correctly calculated.
The slope through (-3,4) and (0,k) is (k-4)/3, which you correctly calculated.
Multiply those slopes and set the product equal to -1.
slope1*slope2 = -1
(1/4)*(k-4)/3 = -1
(k-4)/12 = -1
k-4 = -1*12
k-4 = -12
k = -12+4
k = -8 is the final answer.
Check:
Compute the slope of the line through (-3,4) and (0,-8)
m = (y2-y1)/(x2-x1)
m = (-8-4)/(0-(-3))
m = (-8-4)/(0+3)
m = -12/3
m = -4
This slope of -4 must multiply with the other slope of 1/4 to get a product of -1.
Sure enough (1/4)*(-4) = -1 is indeed the case.
The answer has been verified.
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