Question

Select the most precise name of quadrilateral MNOP given the coordinates of M, N, O, and P.M(1,1)N(3,4)0(6,6)P(4,3)1O parallelogramO rectangleO rhombusO square

Answer 1

Given data:

The given coordinates are M(1,1), N(3,4), O(6,6), P(4,3).

The length MN is,

`\begin{gathered} MN=\sqrt[]{(3-1)^2+(4-1)^2} \\ =\sqrt[]{4+9} \\ =\sqrt[]{13} \end{gathered}`

The length NO is,

`\begin{gathered} NO=\sqrt[]{(6-3)^2+(6-4)^2} \\ =\sqrt[]{9+4} \\ =\sqrt[]{13} \end{gathered}`

The length OP is,

`\begin{gathered} OP=\sqrt[]{(4-6)^2+(3-6)^2} \\ =\sqrt[]{13} \end{gathered}`

The length MP is,

`\begin{gathered} MP=\sqrt[]{(4-1)^2+(3-1)^2} \\ =\sqrt[]{13} \end{gathered}`

The length of diagonal MO is,

`\begin{gathered} MO=\sqrt[]{(6-1)^2+(6-1)^2} \\ =\sqrt[]{25+25} \\ =\sqrt[]{50} \end{gathered}`

The