Question

Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B. a(5, 4) b(0.5, 7) c(0, 6) d(−4, 10)

Answer 1

d. (−4, 10)

Explanation:

The midpoint has the following definition:

`\left(x_m,y_m\right)=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)`

We can calculate point B, using the following equations obtained taking into account the above:

`\begin{gathered} x_m=(x_1+x_2)/(2) \\ \\ -1=(2+x_2)/(2) \\ \\ x_2+2=-2 \\ \\ x_2=-2-2=-4 \\ \\ \\ y_m=(y_1+y_2)/(2) \\ \\ 8=(6+y_2)/(2) \\ \\ y_2+6=16 \\ \\ y_2=16-6=10 \\ \\ \text{ Therefore, point B is located at \lparen-4, 10\rparen} \end{gathered}`

The correct answer is: d. (−4, 10)