Question

The midpoint of AB is M (0, -4). If the coordinates of A are (2, -1), what are thecoordinates of B?

Answer 1

Given:

The midpoint of AB is M

Coordinates of M (0,-4)

Coordinates of A (2.-1)

Find-:

The value of coordinates of B

Explanation-:

The Coordinates of B

Let Coordinates of B is

$B=(x,y)$

The midpoint formula is

$M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where,

$\begin{gathered} (x,y)=\text{ Midpoint} \\ \\ (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}$

The midpoint is

$\begin{gathered} M=(0,-4) \\ \\ A=(2,-1) \\ \\ B=(x,y) \end{gathered}$

So, Midpoint is

$\begin{gathered} (0,-4)=(\frac{2+x}{2},\frac{-1+y}{2}) \\ \\ \end{gathered}$

So, the (x,y) is

$\begin{gathered} \frac{2+x}{2}=0 \\ \\ 2+x=0 \\ \\ x=-2 \end{gathered}$

The value of "y"

$\begin{gathered} \frac{-1+y}{2}=-4 \\ \\ -1+y=-4\times2 \\ \\ -1+y=-8 \\ \\ y=-8+1 \\ \\ y=-7 \end{gathered}$

So the point B is

$B(x,y)=(-2,-7)$