Question

Choose the best selection for the quadrilateral with verticles at the following points: (0,0), (1,3),(5,0,(6,3)

Answer 1

Explanation

We are given the following points:

`(0,0),(1,3),(5,0),(6,3)`

We are required to determine which quadrilateral it is with the given points as vertices.

This is achieved thus:

- The graph of the points is:

- Next, we determine if AB = CD and BC = AD as follows:

`\begin{gathered} A(0,0)\to(x_1,y_1) \\ B(1,3)\to(x_2,y_2) \\ Distance(d)=√((x_2-x_1)^2+(y_2-y_1)^2) \\ AB=√((1-0)^2+(3-0)^2) \\ AB=√(1+9) \\ AB=√(10) \\ \\ C(6,3)\to(x_1,y_1) \\ D(5,0)\to(x_2,y_2) \\ \begin{equation*} Distance(d)=√((x_2-x_1)^2+(y_2-y_1)^2) \end{equation*} \\ CD=√((5-6)^2+(0-3)^2) \\ CD=√(1+9) \\ CD=√(10) \end{gathered}`
`\begin{gathered} B(1,3)\to(x_1,y_1) \\ C(6,3)\to(x_2,y_2) \\ \begin{equation*} Distance(d)=√((x_2-x_1)^2+(y_2-y_1)^2) \end{equation*} \\ BC=√((6-1)^2+(3-3)^2) \\ BC=√(25+0)=√(25) \\ BC=5 \\ \\ A(0,0)\to(x_1,y_1) \\ D(5,0)\to(x_2,y_2) \\ \begin{equation*} Distance(d)=√((x_2-x_1)^2+(y_2-y_1)^2) \end{equation*} \\ AD=√((5-0)^2+(0-0)^2) \\ AD=√(25+0)=√(25) \\ AD=5 \end{gathered}`

- Using the graph and the distances gotten above, the quadrilateral is a Parallelogram.

Option D is correct.