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=((x_A+x_B)/(2),(y_A+y_B)/(2)) \\ (3,0)=((6+x_B)/(2),(-2+y_B)/(2)) \\ 3=(6+x_B)/(2),0=(-2+y_B)/(2) \\ 3=(6+x_B)/(2)\Rightarrow3\cdot2=6+x_B\Rightarrow6=6+x_B_{} \\ x_B=6-6=0_{} \\ x_B=0 \\ \\ 0=(-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}`