SOLUTION: are the lines parallel, perpendicular, or neither? AB: A(0,2) B(3,4) C(2,7) D(-1,5)

Algebra ->  Points-lines-and-rays -> SOLUTION: are the lines parallel, perpendicular, or neither? AB: A(0,2) B(3,4) C(2,7) D(-1,5)      Log On


   

Question 805403: are the lines parallel, perpendicular, or neither? AB: A(0,2) B(3,4) C(2,7) D(-1,5)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
AB is parallel to CD and BC is parallel to AD.
There are no perpendicular lines.
ABCD is a parallelogram, but not a rectangle.

Parallel lines have the same slope. Perpendicular lines have slopes whose product is -1.
slope of AB = %284-2%29%2F%283-0%29=2%2F3 and slope of DC = %287-5%29%2F%283-0%29=2%2F%282%2B1%29=2%2F3
Both slopes are the same, so AB is parallel to DC
slope of BC = %287-4%29%2F%282-3%29=3%2F%28-1%29=-3 and slope of DA = %285-2%29%2F%28-1-0%29=3%2F%28-1%29=-3
Both slopes are the same, so BC is parallel to DA.

The product of the slopes 2%2F3 and -3 is
%282%2F3%29%28-3%29=-2%3C%3E-1 so there are no perpendicular lines in ABCD.

From the drawing (see below) I can tell that it is not a rhombus, because the sides have different length, so diagonals AC and BD are not perpendicular.
AB and CD are sqrt%2813%29 units long.
BC and DA are sqrt%2810%29 units long