Sample Question

Consider the shape formed by joining, in order, the points
F(1, 6), R(4, 2), O(−1, −2 ) and G(−4, 2).

Determine as precisely as possible the nature of the polygon. Justify your claim.
(Saying It looks like a … is not sufficient. You must give confirming information about the polygon.)

Sample Response

I'll plot the points to see the segment and help my thinking.

It looks like a rectangle, but I'll check some properties out.

I see slope_FR = −4/3, slope_GO = −4/3, slope_GF = 4/5, slope_OR = 4/5.

Since the slopes of opposite sides are the same, we have two pairs of parallel sides.
It's a parallelogram!

I know it's not a rectangle though since the slopes of adjacent sides are not opposite reciprocals.