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  4. One end of a line segment is (5,3), the midpoint is (7,2). Find the other co-ordinates of the other end.

Q. One end of a line segment is $(5,3)$, the midpoint is $(7,2)$. Find the other co-ordinates of the other end.

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Solution:

$x_{1} \cdot x_{2} \cdot x_{3} \ldots \cdots \cdot=cis \frac{\pi}{3} \cdot cis \frac{\pi}{3^{2}} \ldots \cdots \cdot$
$=cis \pi\left(\frac{1}{3}+\frac{1}{3^{2}}+\ldots \ldots\right)=cis\left[\pi\left(\frac{1 / 3}{1-1 / 3}\right)\right]$
$\left[\right.$ by $S_{\infty}$ of a g.p.with $\left.r < 1\right]$
$=cis\left(\frac{\pi / 3}{2 / 3}\right)=cis \pi / 2=i$

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