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One endpoint on GH is G(–7, 24). The midpoint is M(3, 4). Find the coordinates of the endpoint H. ( , )

Please help find endpoint H

Respuesta :

semsee45

Answer:

H (13, -16)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given:

  • Endpoint (x₁, y₁) = G (-7, 24)
  • Endpoint (x₂, y₂) = H
  • Midpoint = M (3, 4)

Substitute the given endpoint G and midpoint M into the midpoint formula:

[tex]\implies M=\left(\dfrac{x_H+x_G}{2},\dfrac{y_H+y_G}{2}\right)[/tex]

[tex]\implies (3, 4)=\left(\dfrac{x_H-7}{2},\dfrac{y_H+24}{2}\right)[/tex]

x-value of endpoint H:

[tex]\implies 3=\dfrac{x_H-7}{2}[/tex]

[tex]\implies 6=x_H-7[/tex]

[tex]\implies x_H=13[/tex]

y-value of endpoint H:

[tex]\implies 4=\dfrac{y_H+24}{2}[/tex]

[tex]\implies8=y_H+24[/tex]

[tex]\implies y_H=-16[/tex]

Therefore, the coordinates of endpoint H are:

  • (13, -16)

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