For quadrilateral abcd, determine the most precise name for it. a(2,3), b(12,3), c(8,6) and d(5,6). show your work and explain.

1. Draw the points in the coordinate axes, as in the attached picture.

2. AB and CD are parallel, (both are parallel to the x-axis)

3. A is closer to the y axis than D and C is closer to the C closer than B

4. So combining 2 and 3, we conclude that ABCD is a trapezoid.

5. The remaining thing to check is whether the trapezoid is isosceles or not. For this we drop the heights to AB from points C and D, 

and see that the distances from the feets of these heights to the points A and B are not equal.

Trapezoid