Question

1. higher order thinking one side of a rectangle is parallel to the x - axis. one vertex of the rectangle is located at (5,2) and another vertex at (1,4). what are the coordinates of the other two vertices?

Explanation:

Step1: Analyze the properties of a rectangle

In a rectangle, opposite sides are parallel and equal. Since one side is parallel to the \(x -\)axis, the side perpendicular to it is parallel to the \(y -\)axis.

Step2: Find the coordinates of the other vertices

If one vertex is \((5,2)\) and another is \((1,4)\):

• For the vertex parallel to \((5,2)\) along the \(y -\)axis (since the side perpendicular to the \(x -\)axis is parallel to the \(y -\)axis) with the same \(x -\)coordinate as \((1,4)\), we get \((1,2)\) (because the \(y -\)coordinate is the same as in \((5,2)\) for the parallel - to - \(x -\)axis side).
• For the vertex parallel to \((1,4)\) along the \(y -\)axis with the same \(x -\)coordinate as \((5,2)\), we get \((5,4)\) (because the \(y -\)coordinate is the same as in \((1,4)\) for the side parallel to the side connecting \((1,4)\) and \((1,2)\)).

Answer:

The other two vertices are \((1,2)\) and \((5,4)\)