Question

classify the quadrilateral shown on the graph. rectangle trapezoid square rhombus

Explanation:

Step1: Recall properties of quadrilaterals

A rectangle has four right - angles, a square is a rectangle with all sides equal, a trapezoid has one pair of parallel sides, and a rhombus has all sides equal.

Step2: Check side - length and angle properties

Let the vertices of the quadrilateral be \(A(- 5,0)\), \(B(0,4)\), \(C(5,0)\), \(D(0,-4)\).
The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(AB=\sqrt{(0 + 5)^2+(4 - 0)^2}=\sqrt{25 + 16}=\sqrt{41}\).
\(BC=\sqrt{(5 - 0)^2+(0 - 4)^2}=\sqrt{25 + 16}=\sqrt{41}\).
\(CD=\sqrt{(0 - 5)^2+(-4 - 0)^2}=\sqrt{25 + 16}=\sqrt{41}\).
\(DA=\sqrt{(-5 - 0)^2+(0 + 4)^2}=\sqrt{25 + 16}=\sqrt{41}\). So all sides are equal.
The slope of \(AB\) is \(m_{AB}=\frac{4-0}{0 + 5}=\frac{4}{5}\), the slope of \(BC\) is \(m_{BC}=\frac{0 - 4}{5 - 0}=-\frac{4}{5}\), \(m_{AB}\times m_{BC}
eq - 1\), so the angles are not right - angles.
Since all sides are equal and the angles are not right - angles, it is a rhombus.

Answer:

Rhombus