Question

Point A is at (3, 4) and point M is at (1, 0). Point M is the midpoint of segment AB. What

are the coordinates of Point B

Answer 1

B (-1 , -4)

Explanation:

A (3 , 4)

M (1 , 0)

`B\left( x_(B),y_(B)\right)`

M is the midpoint of segment AB means :

`\begin{cases}(x_(A)+x_(B))/(2) =x_(M)&\\ (y_(A)+y_(B))/(2) =y_(M)}{} &\end{cases}`

Then

`\begin{cases}x_(B)=2x_(M)-x_(A)&\\ y_(B)=2y_(M)-y_(A)&\end{cases}`

Then

`\begin{cases}x_(B)=2\left( 1\right) -3&\\ y_(B)=2(0)-4&\end{cases}`

Then

`\begin{cases}x_(B)=-1&\\ y_(B)=-4&\end{cases}`