Question

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.

Answer 1

I asked my teacher for help, but I still don't get it. I need help working through it.

Answer 2

One direct method would be to use the property that diagonals of a parallelogram bisect each other. Check whether the midpoint of 2 points taken at a time equals the midpoint of other two.

Another way is to evaluate distances of each side and check for 2 opp sides equal.

Answer 3

so a parallelogram should have:
parallel sides
opposite sides should be the same length
diagonals biisect one another

Answer 4

so therefore the midpoint of one angle should be equal to another,
you should use the distance formula to see if opposite sides are equal
and use the slope formula to check if the slopes are the same which will tell you the sides are parallel

Answer 5

if you draw it out , it'll become a lot clearer