SOLUTION: line 1 passes through the points (1,-2) and (-2,-4) line 2 passes through the points (2,2) and (0,5) is the prependicular or parallel

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Question 128875: line 1 passes through the points (1,-2) and (-2,-4)
line 2 passes through the points (2,2) and (0,5)
is the prependicular or parallel
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!





Discussion







The equation of a line passing through two points is given by y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B2%5D%29.

You need to derive the equations for both of your

lines and then put them into slope-intercept form y=mx%2Bb, so that you can

compare the slope numbers for the two lines.





Lines are parallel if and only if their slopes are equal, i.e. m%5B1%5D=m%5B2%5D.





Lines are perpendicular if and only if their slopes are negative reciprocals,

i.e. m%5B1%5D=-1%2Fm%5B2%5D 










Solution







Line 1:

y-%28-2%29=%28%28%28-2%29-%28-4%29%29%2F%281-%28-2%29%29%29%28x-%28-2%29%29

y%2B2=%282%2F3%29%28x%2B2%29

y%2B2=2x%2F3%2B4%2F3

y=2x%2F3-2%2F3



Line 2:

y-2=%28%282-5%29%2F%282-0%29%29%28x-2%29

y-2=%28-3%2F2%29%28x-2%29

y-2=-3x%2F2%2B3

y=-3x%2F2%2B5





The slope of Line 1 is 2%2F3.  The negative reciprocal of 2%2F3 is -3%2F2 which is the slope of Line 2.



Therefore the lines are perpendicular.














Check Answer







They look perpendicular to me: