Question

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

Answer 1

Point M divides line segment AB in their midpoint.

This means that the segments AM and MB have the same length.

Be A(-4, 2) and M(-5,4) the coordinates of endpoint A and midpoint M:.

First step is to plot both poins and line segment AM:

To determine the coordinates of endpoint B, first you have to determine the distance between A and M with respect to their y-coordinates and x-coordinates.

Distance over the x-coordinates:

`d_x=x_M-x_A=(-4)-(-5)=-4+5=1`

Next subtract this distance to the x-coordinate of M to calculate the x-coordinate of B:

`x_B=x_M-d_x=-5-1=-6`

Distance over the y-axis:

`d_y=y_M-y_A=4-2=2`

Next add it to the y-coordinate of M to calculate the y-coordinate of B:

`y_B=y_M+d_y=4+2=6`

The coordinates of B are:

`B(-6,6)`