Question

If the coordinates of A are (6, -2) and the midpoint of AB is (3,0), determine the coordinates of the other endpoint B. (4.5, -1) (0, 2) (2, 1.5) (3.0.5)

Answer 1

Let's begin by listing out the information given to us:

$\begin{gathered} AB=(6,-2) \\ Midpoint(AB)=(3,0) \end{gathered}$

We are to calculate for the coordinates of B

The formula for calculating the midpoint is given by:

$\begin{gathered} M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2}) \\ (3,0)=(\frac{6+x_B}{2},\frac{-2+y_B}{2}) \\ 3=\frac{6+x_B}{2},0=\frac{-2+y_B}{2} \\ 3=\frac{6+x_B}{2}\Rightarrow3\cdot2=6+x_B\Rightarrow6=6+x_B_{} \\ x_B=6-6=0_{} \\ x_B=0 \\ \\ 0=\frac{-2+y_B}{2}\Rightarrow2\cdot0=-2+y_B\Rightarrow0=-2+y_B \\ y_B=0+2=2 \\ y_B=2 \\ \\ \therefore B(x,y)=(0,2) \end{gathered}$