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.

Explanation:

It is given that,

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

Since,

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Then,

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

Also,

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

Since,

$EF\perp GF$

Then,

$Slope\text{ }of\text{ }EF=-\frac{2}{5}$

Also,

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

That implies,

$\begin{gathered} Length\text{ }of\text{ }HE=Length\text{ }of\text{ }GF=\sqrt{29} \\ =5.39 \end{gathered}$

Also,

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

Then,

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

Hence,

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