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

1 Answer
Daniel L.
Nov 15, 2015

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#

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