Question

The midpoint of AB is M(-3,2). If the coordinates of A are (-5,-4) what are the coordinates of B

Answer 1

The x and y-coordinates of the midpoint of a segment are given by the following formulas:

`xm=(xA+xB)/(2)`
`ym=(yA+yB)/(2)`

Where (xm, ym) is the idpoint, (xA, yA) are point A coordinates and (xB, yB) are point B coordinates.

From the first equation, we can solve for xB:

`\begin{gathered} xm=(xA+xB)/(2) \\ 2xm=xA+xB \\ 2xm-xA=xB \\ xB=2xm-xA \end{gathered}`

Similarly for yB:

`yB=2ym-yA`

By replacing -5 for xA and -3 for xm in the first equation, we get:

`\begin{gathered} xB=2*(-3)-(-5) \\ xB=-6+5 \\ xB=-1 \end{gathered}`

Replacing -4 for yA and 2 for ym in the second equation, we get:

`\begin{gathered} yB=2*(2)-(-4) \\ yB=4+4 \\ yB=8 \end{gathered}`

Then, yB equals 8.

Then, the coordinates of point B are (-1, 8)