Question

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

Answer 1

Answer: 13 -16

Step-by-step explanation: Edge 2023

Answer 2

H (13, -16)

Explanation:

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

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:

`\implies M=\left((x_H+x_G)/(2),(y_H+y_G)/(2)\right)`

`\implies (3, 4)=\left((x_H-7)/(2),(y_H+24)/(2)\right)`

x-value of endpoint H:

`\implies 3=(x_H-7)/(2)`

`\implies 6=x_H-7`

`\implies x_H=13`

y-value of endpoint H:

`\implies 4=(y_H+24)/(2)`

`\implies8=y_H+24`

`\implies y_H=-16`

Therefore, the coordinates of endpoint H are:

• (13, -16)