Question

[5.03] Given points A(4, 3), B(4, -2), C(-4, -1), D(-1, 4). Determine whether quadrilateral ABCD with the given vertices is a parallelogram or not. You must provide work to prove your answer. Your help will be greatly appreciated.

Answer 1

probably the first thing you should be asking yourself is: does |AB| = |CD| and |BC| = |AD|

Answer 2

If it is a parallelogram then the opposite sides will be parallel. That means the slopes will be the same (equal) I think you should examine the segments CD and AB to see if they have the same slope.

Answer 3

Sincer slope is equal to:\[\Delta y \over \Delta x\] It is easy to determine this.

Answer 4

CD, slope (m) would be (-1-4)/(-4-(-1))=-5/-3=5/3 now if AB has the same slope (5/3 that means they are parallel, if not they aint.

Answer 5

Lets check and see AB, slope (m) is (3-(-2))/(4-4) Oh Oh Oh!!!,has an undefined slope it is a vertical line, so no no, it is not a parallelogram.

Answer 6

You see the (4-4) IS 0 and division by 0 results in "undefined"

Answer 7

THANK YOU SO MUCH !! :)

Answer 8

You're welcome, the method offered by gordonj005 would of worked also, but involved using the distance formula which is more complicated.