Question

ke shawn is placing a right triangle in the coordinate plane. he knows that the longer leg is twice the length of the shorter leg. he places the longer leg on the x - axis. what coordinates should he assign to the third vertex of the triangle? enter your answer in the boxes

Explanation:

Step1: Determine the length of the shorter leg

Since the longer leg is on the \(x -\)axis and the longer leg is twice the length of the shorter leg. The length of the longer leg is from \((0,0)\) to \((2a,0)\) (assuming the length of the shorter leg is \(a\)). Given the shorter - leg length (the \(y -\)coordinate of the vertex \((0,a)\)), if the longer leg (along the \(x -\)axis) has a length \(l\) and \(l = 2a\).

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

The third vertex is on the \(x -\)axis. The length of the longer leg (along the \(x -\)axis) is \(2a\). Since one end of the longer leg is at \((0,0)\), the other end (the third vertex of the right - triangle, because the right - angle is at \((0,0)\) as one leg is on the \(x -\)axis and the other is on the \(y -\)axis) has an \(x -\)coordinate equal to the length of the longer leg. The \(y -\)coordinate of the vertex on the \(x -\)axis is \(0\).

Answer:

\((2a,0)\)