Given one endpoint and midpoint in (x,y) of a line segment, explain how to find the other end point.

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It's very very simple:

The midpoint formula give you: $$ M=(x_m,y_m)=\left( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right) $$ where $(x_1,y_1)$ are the coordinates of a point, say your $C$, and $(x_2,y_2)$ are the coordinate of the oter point, i.e the point $D$ that you are searching.

So, substituting the given coordinates you have:

$$ 4=\dfrac{6+x_2}{2} \quad \land \quad 2=\dfrac{5+y_2}{2} $$ Now can you solve these two simple equations?


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

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Arthur Alex Karapetov
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Arthur Alex Karapetov

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Updated on July 22, 2022

Comments

  • Arthur Alex Karapetov
    Arthur Alex Karapetov over 1 year

    A line segment with one end at C(6,5)has midpoint M(4,2). Determine the coordinates of the other endpoint, D. Explain your solution and describe a method to check your answer.

  • Arthur Alex Karapetov
    Arthur Alex Karapetov over 8 years
    How can you solve these two simple equations? Can you please finish, with steps.
  • Emilio Novati
    Emilio Novati over 8 years
    Don't you know how solve a linear equation such these?
  • Arthur Alex Karapetov
    Arthur Alex Karapetov over 8 years
    Would you please do it I'm not sure . I'm a grade 8 student doing grade 10 work without a teacher.
  • Emilio Novati
    Emilio Novati over 8 years
    See my edit. But you have to do some work... And not forget to accept the answer!