Year 11 Maths - Methods Linear Relations

Bisection and Lengths of Line Segments

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Questions

Question 1

17637

The midpoint of \(PQ\) has the co - ordinates \({\rm{(}}4, - 1).\,\) \(P\) is the point \({\rm{(3}}, - 4),\,\,Q\) is the point?

Answer

\(Q(5,2)\)

Worked Solution

\begin{align}
&\text{Let } Q \text{ have the coordinates } \left(x_{2}, y_{2}\right)\\
&\begin{aligned}
\therefore \frac{3+x_{2}}{2} &=4,& \frac{-4+y_2}{2}&=-1 \\
3+x_{2} &=8 &-4+y_2&=-2 \\
x_{2} &=5 & y_{2}&=2
\end{aligned}\\
&\rightarrow Q(5,2)
\end{align}

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