Question

A line segment CD has one endpoint C (6,5) and midpoint M (4,2) How do you determine point D?

Answer 1

Point `D` has coordinates: `D=(2,-1)`

Explanation:

All you have to do is use the formula for coordinates of a midpoint of a line segment. If the segment's ends are `A=(x_A,y_A)` and `B=(x_B,y_B)`, then the midpoint has coordinates:

`M=((x_A+x_B)/2;(y_A+y_B)/2)`

In this case midpoint `M` and one end `C` is given, so you can write, that:

`x_M=(x_C+x_D)/2`, so

`4=(6+x_D)/2`

`8=6+x_D`

`x_D=2`

If you rerpeat this procedure for `y` coordinate you will get:

`y_D=-1`

Note:

If the task was given in `3D` space the algorythm would be the same. The only difference would be the number of coordinates - you woul have to add the formula:

`z_M=(z_A+z_B)/2`