Question

The midpoint of AB is M(3, 1). If the coordinates of A are (1, -1), what are the coordinates of B?

Answer 1

Answer:

B(5,3)

Explanation:

Given a line segment AB with endpoints A and B defined below, the midpoint, M is obtained using the formula:

$\begin{gathered} M(x,y)=(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}) \\ A(x_1,y_1),B(x_2,y_2) \end{gathered}$

Given that:

• Midpoint=M(3,1)

,

• Coordinates of A are (1, -1)

Substitution into the formula gives:

$\begin{gathered} M(3,1)=(\dfrac{x_2+1}{2},\dfrac{y_2-1}{2}) \\ \implies\dfrac{x_2+1}{2}=3 \\ \implies x_2+1=3\times2 \\ \implies x_2+1=6 \\ \implies x_2=6-1 \\ \implies x_2=5 \\ Similarly\colon \\ \dfrac{y_2-1}{2}=1 \\ \implies y_2-1=2 \\ \implies y_2=1+2 \\ \implies y_2=3 \end{gathered}$

Therefore, the coordinates of B are (5,3).