Question

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. (, )

Explanation:

Step1: Determine the length of the longer side

Since the longer side is 3 times the shorter side and the shorter side has length \(a\) (from the \(y\) - coordinate \((0,a)\)), the length of the longer side is \(3a\).

Step2: Find the \(x\) - coordinate of the top - right vertex

The rectangle has one side along the \(x\) - axis. Starting from \((0,a)\), moving along the \(x\) - direction (horizontal direction) by the length of the longer side. The \(x\) - coordinate of the top - right vertex is \(3a\) (because the length of the side parallel to the \(x\) - axis is \(3a\)), and the \(y\) - coordinate remains the same as the \(y\) - coordinate of the point \((0,a)\) (since it is a rectangle and the sides parallel to the \(y\) - axis are vertical, so there is no change in the \(y\) - value for the top - side vertices).

Answer:

\((3a,a)\)