Question

Hi can you please help me out all the tabs for this question have the same options

Answer 1

Given

To find the slope and length of each side.

Step-by-step explanation:

It is given that,

`H(-3,-2),G(2,-4),F(4,1),E(-1,3)`

Since,

`Slope=(y_2-y_1)/(x_2-x_1)`

Then,

`\begin{gathered} Slope\text{ }of\text{ }HE=(3-(-2))/(-1-(-3)) \\ =(3+2)/(-1+3) \\ =(5)/(2) \end{gathered}`
`\begin{gathered} Slope\text{ }of\text{ }HG=(-4-(-2))/(2-(-3)) \\ =(-4+2)/(2+3) \\ =-(2)/(5) \end{gathered}`

Also,

`\begin{gathered} Slope\text{ }of\text{ }GF=(1-(-4))/(4-2) \\ =(1+4)/(2) \\ =(5)/(2) \end{gathered}`

Since,

`EF\perp GF`

Then,

`Slope\text{ }of\text{ }EF=-(2)/(5)`

Also,

`\begin{gathered} Length\text{ }of\text{ }HE=√((-3-(-1))^2+(3-(-2))^2) \\ =√((-3+1)^2+(3+2)^2) \\ =√((-2)^2+5^2) \\ =√(4+25) \\ =√(29) \end{gathered}`

That implies,

`\begin{gathered} Length\text{ }of\text{ }HE=Length\text{ }of\text{ }GF=√(29) \\ =5.39 \end{gathered}`

Also,

`\begin{gathered} Length\text{ }of\text{ }HG=√((-3-2)^2+(-2-(-4))^2) \\ =√((-5)^2+(-2+4)^2) \\ =√(25+4) \\ =√(29) \\ =5.39 \end{gathered}`

Then,

`Length\text{ }of\text{ }HG=Length\text{ }of\text{ }EF=5.39`

Hence,