Question

draw the polygon whose vertices are $(1,-7),(1,0),(4,0)$, and $(4,-7)$. then choose the best description of the polygon from the choices below.

Explanation:

Step1: Analyze the properties of the polygon

Plot the points \((1, - 7)\), \((1,0)\), \((4,0)\), and \((4,-7)\) on the coordinate plane.

• For the vertical sides:

The two points \((1, - 7)\) and \((1,0)\) have the same \(x\) - coordinate (\(x = 1\)). Using the distance formula \(d=\vert y_2 - y_1\vert\), the length of this vertical side is \(\vert0-(-7)\vert=7\).
The two points \((4, - 7)\) and \((4,0)\) have the same \(x\) - coordinate (\(x = 4\)). The length of this vertical side is \(\vert0-(-7)\vert = 7\).

• For the horizontal sides:

The two points \((1,0)\) and \((4,0)\) have the same \(y\) - coordinate (\(y = 0\)). Using the distance formula \(d=\vert x_2 - x_1\vert\), the length of this horizontal side is \(\vert4 - 1\vert=3\).
The two points \((1,-7)\) and \((4,-7)\) have the same \(y\) - coordinate (\(y=-7\)). The length of this horizontal side is \(\vert4 - 1\vert=3\).

Step2: Check the angles

Since the sides are either vertical (parallel to the \(y\) - axis) or horizontal (parallel to the \(x\) - axis), the adjacent sides are perpendicular to each other (the product of the slopes of a vertical line \(x = a\) (undefined slope) and a horizontal line \(y = b\) (slope \(m = 0\)) is \(m_1\times m_2=\infty\times0\) which implies they are perpendicular in the geometric sense). And opposite sides are equal in length (\(3\) and \(7\)).

Answer:

Rectangle