SOLUTION: points A(3,4), B(-1,3), C (-2,-5) and D( a, -1) are the four points on a cartesian plane. find a if: AB is parallel to CD AB is perpendicular to CD

Algebra ->  Coordinate-system -> SOLUTION: points A(3,4), B(-1,3), C (-2,-5) and D( a, -1) are the four points on a cartesian plane. find a if: AB is parallel to CD AB is perpendicular to CD      Log On


   

Question 800955: points A(3,4), B(-1,3), C (-2,-5) and D( a, -1) are the four points on a cartesian plane. find a if:
AB is parallel to CD
AB is perpendicular to CD
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
slope of AB
x1 y1 x2 y2
3 4 -1 3

slope m = (y2-y1)/(x2-x1)
( 3 - 4 )/( -1 - 3 )
( -1 / -4 )
m= 1/ 4

Slope of CD
(-5-(-1))/(-2-a)
=-4/(-2-a)
parallel lines have same slopes
-4/(-2-a)=1/4
-16=-2-a
a=14
____________________
When lines are perpendicular the slopes are negative reciprocal of each other
So CD will have slope of -4
-4/(-2-a)=-4
-4=8+4a
4a=-12
a=-3