Quadrilateral ABCD has vertices A (–3, 3), B (2, 5), C (5, 2), and D (0, 0). Using slope, distance, and/or midpoints, classify ABCD as a rectangle, rhombus, square, trapezoid, or isosceles trapezoid.

Question

I don't understand this that much. I got the formula and everything but I don't understand how to find if its a rectangle, rhombus, etc.

Answer 1

it's a rhombus or parallelogram, opposite sides are parallel & equal length. Just plot it, and you can quickly see it.

also, 2 right angles are formed by the top side with a horizontal line, same with bottom side & horizontal, with each tangent of the angle formed = 2/5

origin (0,0) to (5,2) has slope = 2/5 = tangent of the angle or the "rise over the run" change in y coordinates divided by change in x coordinates (2-0)/(5-0) = 2/5

(-3,3) to (2,5) similarly has slope =(5-3)/(2--3) = 2/5

but all 4 sides are not equal, so it's not a rhombus, but it is a parallelogram