Question

A trapezoid with an area of 45 square units is plotted on the coordinate plane. This trapezoid can be decomposed into a rectangle and right triangle. The vertices of the rectangle are located at the points (–6, –2),(–6, 3), (1,3), and (1,–2). Write two possible coordinates for the last vertex of the trapezoid that have different x-coordinates. Show your work in the space below or on the coordinate plane.

Answer 1

We know that the trapezoid can be decomposed into a rectangle and a right triangle. The rectangle has two sides with length 7 (the difference between the y-coordinates of the top and bottom vertices) and 8 (the difference between the x-coordinates of the right and left vertices), so its area is 56 square units. Therefore, the area of the right triangle is 45 - 56 = -11 square units, which is impossible. Hence, there must be an error in the problem statement or in the way it was transcribed. Without additional information, it is not possible to provide two possible coordinates for the last vertex of the trapezoid that have different x-coordinates.