SOLUTION: 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 perpe

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(52890) (Show Source): You can put this solution on YOUR website!
.
In your post, in the first phrase, you mention the Line L twice, which is a MISTAKE, obviously.

Fix the error and re-post.

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).

RELATED QUESTIONS
``Line L, passes through points P(n, 4) and Q(1 2), Line L, passes through points R(4, 3) (answered by josgarithmetic)
``Line L, passes through points P(n, 4) and Q(1 2), Line L, passes through points R(4, 3) (answered by josgarithmetic)
`Line line 1, passes through points P(n, 4) and Q(1 2), Line 2, passes through points... (answered by josgarithmetic)
1)line l passes through point (9,1) and line p is the graph 3x-7y=22. If l 1p, what is... (answered by josgarithmetic)
a line l with a slope of 1/4 passes through the points (0,1/20 and (4,y). What is the... (answered by Alan3354)
What is the slope of a line that passes through points (-2 -1) and (4... (answered by Fombitz)
Line L passes through the points (-2,0) and (0,a). Line LL passes through the points... (answered by mananth)
1) Find the exact solution of the equation: 32/e^x - e^2x = 4 2) A... (answered by solver91311)
the slope of a line is 1/2. If the line passes through the points (0, k) and (5, 4), what (answered by stanbon)