Question

What is the most precise name of this quadrilateral? A(1,8) B(4,6) C(1,-2) D(-2,0)

Answer 1

On actual quad paper it would look much ore obvious if this is a rectangle or parallelogram. But to know this more precisely, you can check the slope of the lines at each corner and see if the product of the slopes of the lines give -1. If it does, the lines are perpendicular implying that you have right angles, and hence a rectangle.

If the product of the slopes is not -1, then you have a parallelogram, provided that the two opposite corners have the same slope products

Now I say parallelogram or rectangle because the angles don't look obvious, but the lengths kind of do. But to be sure about this, you would measure the length of each side (you can easily do this by Pythagoras). But again, if you did the step above to check the slopes, if you have the same slop products at opposite angles, you will have two congruent opposite angles, implying that you have two opposite equal-length sides.