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# Q(0, 7, −6) and M(−1, 3, 2), where M is the midpoint of the line segment PQ

Solution

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Answered 9 months ago
Answered 9 months ago
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Let $P=(x,y,z)$ be the initial point.

Given that $Q=(0,7,-6)$ be the terminal point and $M=(-1,3,2)$ be the mid point of the line segment $PQ$.

Therefore,

\begin{aligned} &\left(\dfrac{x+0}{2},\dfrac{y+7}{2},\dfrac{z-6}{2}\right)=(-1,3,2)\\ \implies&\dfrac{x}{2}=-1,~\dfrac{y+7}{2}=3,~\dfrac{z-6}{2}=2\\ \implies&x=-2,~y+7=6,~z-6=4\\ \implies& x=-2,~y=-1,~z=10 \end{aligned}

So, the initial $P =(-2,-1,10)$.

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