Q:

# Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis. What coordinates should she assign to the top-right vertex of the rectangle? Enter your answer in the boxes. ( , ) A rectangle is in the coordinate plane so that the bottom left vertex is at 0 comma 0, the top left vertex is on the positive side of the y-axis and is labeled 0 comma a, the top right vertex is in the first quadrant and is labeled question mark comma question mark, and the bottom right vertex is on the positive side of the x-axis.

Accepted Solution

A:
(3a, a) The problem states that the longer side of the rectangle is placed on the x-axis. Additionally, the problem states that the coordinate (0,0) is the bottom left vertex. That tells you that you don't have any translation going on, so you don't have to add a constant to either the X, or Y value. Finally, the problem states that the upper left vertex is at coordinate (0,a). Because of that and the fact that the lower left coordinate is at (0,0), the length of the shorter side of the rectangle has to be a. And three times the length of "a" is "3a". So the upper right coordinate has to have an X value of "3a" and a Y value of "a", or in other words (3a,a).