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

Nov 15, 2015

Point $D$ has coordinates: $D = \left(2 , - 1\right)$

#### 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 $A = \left({x}_{A} , {y}_{A}\right)$ and $B = \left({x}_{B} , {y}_{B}\right)$, 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:

${x}_{M} = \frac{{x}_{C} + {x}_{D}}{2}$, so

$4 = \frac{6 + {x}_{D}}{2}$

$8 = 6 + {x}_{D}$

${x}_{D} = 2$

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

${y}_{D} = - 1$

Note:

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

${z}_{M} = \frac{{z}_{A} + {z}_{B}}{2}$