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You are watching: How to find one endpoint from an endpoint and a midpoint

A heat segment v one end at C(6,5)has midpoint M(4,2). Determine the works with of the various other endpoint, D. Define your solution and also describe a an approach to check your answer.


It"s very very simple:

The midpoint formula give you:$$M=(x_m,y_m)=left( dfracx_1+x_22,dfracy_1+y_22 ight)$$where $(x_1,y_1)$ are the works with of a point, say your $C$, and also $(x_2,y_2)$ space the coordinate of the oter point, i.e the point $D$ the you space searching.

So, substituting the given collaborates you have:

$$4=dfrac6+x_22 quad land quad 2=dfrac5+y_22$$Now have the right to you solve these two simple equations?

$$4cdot 2=6+x_2 Rightarrow 8-6=x_2 Rightarrow x_2=2$$$$2 cdot 2=5+y_2 Rightarrow 4-5=y_2 Rightarrow y_2=-1$$

edited Mar 5 "17 in ~ 19:23

A. Salguero-Alarcón
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answer Mar 5 "15 in ~ 22:08

Emilio NovatiEmilio Novati
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