SOLUTION: Line A goes through the points (2, #) and (-4, 21). Line B goes through the points (4, -1) and (10, 1). Are these two lines parallel, perpendicular, or neither?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Line A goes through the points (2, #) and (-4, 21). Line B goes through the points (4, -1) and (10, 1). Are these two lines parallel, perpendicular, or neither?      Log On


   

Question 110696This question is from textbook
: Line A goes through the points (2, #) and (-4, 21). Line B goes through the points (4, -1) and (10, 1). Are these two lines parallel, perpendicular, or neither? This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume that you meant point (2,3) for the first point of line A since '#' is Shift-3.
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Step 1 is to calculate the slopes of each line:
:
m%5BA%5D=%2821-3%29%2F%28-4-2%29=18%2F-6=-3, and
:
m%5BB%5D=%281-%28-1%29%29%2F%2810-4%29=2%2F6=1%2F3
:
Line A is parallel to line B if and only if m%5BA%5D=m%5BB%5D, but -3%3C%3E1%2F3 so line A is NOT parallel to line B.
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Line A is perpendicular to line B if and only if m%5BA%5D=-1%2Fm%5BB%5D. Since -3=%28-1%29%2F%281%2F3%29, line A IS perpendicular to line B.
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And they look perpendicular to me.
graph%28400%2C400%2C0%2C6%2C-3%2C3%2C%28-3%29x%2B9%2C%281%2F3%29x-%287%2F3%29%29
:
Extra credit: Write back and tell me which line, red or green, is Line A.