Question

For quadrilateral abcd, determine the most precise name for it. A(-2,3),B(9,3),C(5,6)D(2,6). Show your work and explain.

Answer 1

ABCD is an isosceles trapezoid.

Explanation:

The line AB will be horizontal (parallel to the x axis), because the y values are both 3. It is 9--2 = 11 units long.

CD is also parallel to the x axis because the y values of C and D are both 6. Itis 5 - 2 = 3 units long.

The x values of the four points are all different so ABCD is a trapezoid.

Let's check the lengths of the line segments AC and BD:

AC = √((5--2)^2 + (6-3)^2 = √58.

BD = √((9-2)^2 + (3-6)^2 = √58.

They are equal in length so:

ABCD is an isosceles trapezoid.