Question

Prove that the following vertices form a parallelogram by showing that the opposite sides are parallel.



(1 point)
Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The slope of SA is Press enter key to drop response here.Response input area

The slope of AN is Press enter key to drop response here.Response input area

The slope of ND is Press enter key to drop response here.Response input area

The slope of DS is Press enter key to drop response here.Response input area

Is this a parallelogram? Press enter key to drop response here.Response input area. I know this because the opposite sides of the quadrilateral are parallel.

Answer 1

I don’t see the coordinates or the diagram for S, A, N, D. I can’t compute the slopes without them — please paste the coordinates (or an image) of S, A, N, D.

Meanwhile, here is how to do it yourself:

- Slope formula: m = (y2 − y1) / (x2 − x1).
- Compute m(SA) using coordinates of S and A.
- Compute m(AN) using A and N.
- Compute m(ND) using N and D.
- Compute m(DS) using D and S.

If m(SA) = m(ND) and m(AN) = m(DS), then opposite sides are parallel and S,A,N,D form a parallelogram.

Example (illustration):
- Let S(1,2), A(4,5), N(7,2), D(4,−1).
- m(SA) = (5−2)/(4−1) = 3/3 = 1
- m(AN) = (2−5)/(7−4) = −3/3 = −1
- m(ND) = (−1−2)/(4−7) = −3/(−3) = 1
- m(DS) = (2−(−1))/(1−4) = 3/(−3) = −1
- Here m(SA) = m(ND) and m(AN) = m(DS), so the quadrilateral is a parallelogram.

If you give the actual coordinates I’ll compute the four slopes and conclude whether it’s a parallelogram.