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.
Given one endpoint and midpoint in (x,y) of a line segment, explain how to find the other end point.
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2Do you know the midpoint formula? – Emilio Novati Mar 05 '15 at 21:35
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M=x1+x2/2,y1+y2/2 if you know how to solve the question please do so and with all steps. – Arthur Alex Karapetov Mar 05 '15 at 21:50
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1So, use this formula With the coordinate of $M$ (mid point) and of $D$ ($x_1,y_1$) and find the coordinates of $D=(x_2,y_2)$. – Emilio Novati Mar 05 '15 at 21:53
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Please solve it and show all the steps. – Arthur Alex Karapetov Mar 05 '15 at 21:59
1 Answers
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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?
$$ 4\cdot 2=6+x_2 \Rightarrow 8-6=x_2 \Rightarrow x_2=2 $$ $$ 2 \cdot 2=5+y_2 \Rightarrow 4-5=y_2 \Rightarrow y_2=-1 $$
A. Salguero-Alarcón
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Emilio Novati
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How can you solve these two simple equations? Can you please finish, with steps. – Arthur Alex Karapetov Mar 05 '15 at 22:11
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Would you please do it I'm not sure . I'm a grade 8 student doing grade 10 work without a teacher. – Arthur Alex Karapetov Mar 05 '15 at 22:17
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See my edit. But you have to do some work... And not forget to accept the answer! – Emilio Novati Mar 05 '15 at 22:23