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

ANSWER:

d. (−4, 10)

STEP-BY-STEP EXPLANATION:

The midpoint has the following definition:

$\left(x_m,y_m\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

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

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

The correct answer is: d. (−4, 10)