Question 1106028: Line L, passes through points P(n, 4) and Q(1 2), Line L, passes through points R(4, 3) and S (1, 5). a) What is the value of n if the lines are parallel? b) If the lines are perpendicular, what is the value of n?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884)   (Show Source):
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Obviously you are talking about two different lines., The line through points R and S is fixed, so let's call that the "original" line L. Then let's make M the line through P and Q parallel to line L and N the line through P and Q perpendicular to line L.
The slope of the fixed line L is  .
The slope of the first line is  .
For the lines to be parallel, the slope of the first line has to be -2/3 -- the same as the slope of line L:
The lines are parallel when n is -2; line M passes through the points (-2,4) and (1,2).
For the lines to be perpendicular, the slope of the first line has to be 3/2 -- the negative reciprocal of the slope of line L:
The lines are perpendicular when n is 7/3; line N passes through the points (7/3,4) and (1,2).
The graph shows the original line L (red), passing through (1,5) and (4,3); line M which is parallel to L (green), passing through (-2,4) and (1,2); and line N which is perpendicular to L, passing through (1,2) and (7/3,4).
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