The midpoint of gh is m(4,-3). One endpoint is G(-2,2). Find the coordinates of endpoint H

Mathematics

1 answer:

Mars2501 [29]3 years ago

4 0

Answer:

Step-by-step explanation:

(-2 + x)/2= 4

-2 + x = 8

x = 10

(2 + y)/2 = -3

2 + y = -6

y = -8

(10, -8) for endpoint H

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$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}$

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$\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}$

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The fraction that satisfies the request is $\bf{\dfrac{20}{28}}$ , since in $\bf{\dfrac{-20}{-28}}$ the negative signs are canceled and the first fraction is obtained.