Question

AB has endpoint A(-3,-5) and midpoint M(2,-1).Find the coordinate (x,y) of B.

Answer 1

By definition, the formula to find a Midpoint is:

`M=((x_1+x_2)/(2)+(y_2-y_1)/(2))`

Where the coordinates of the first point are:

`(x_1,y_1)`

And the coordinates of the second point is:

`(x_2,y_2)`

Let be the coordinates of the Midpoint:

`(x_M,y_M)`

In this case, knowing coordinates of the point A and the Midpoint, you can set up the following equations:

- Equation 1:

`x_M=(x_A+x_B)/(2)`

- Equation 2:

`y_M=(y_A+y_B)/(2)`

Choose the Equation 1, substiutute values and solve for x-coordinate of the endpoint B:

`\begin{gathered} x_M=(x_A+x_B)/(2) \\ \\ 2=(-3+x_B)/(2) \\ \\ (2)(2)=-3+x_B \\ 4+3=x_B \\ x_B=7 \end{gathered}`

Now choose the Equation 2 and solve for the y-coordinate of the point B:

`\begin{gathered} y_M=(y_A+y_B)/(2) \\ \\ -1=(-5+y_B)/(2) \\ \\ (-1)(2)=-5+y_B \\ -2+5=y_B \\ y_B=3 \end{gathered}`

Therefore, the coordinates of P are:

`B(7,3)`