Question

find the midpoint of mn if point m is the square root of 2 and -1, point n is 3 square root of 2 and -5

Answer 1

m is at

`m=\sqrt[]{2}-1`

and n is at

`n=3\sqrt[]{2}-5`

Hence the midpoint is at

`\text{midpoint}=(n+m)/(2)`

by substituying the given values, we have

`\text{midpoint}=\frac{(\sqrt[]{2}-1)+(3\sqrt[]{2}-5)}{2}`

which is equal to

`\begin{gathered} \text{midpoint}=\frac{\sqrt[]{2}-1+3\sqrt[]{2}-5}{2} \\ \text{midpoint}=\frac{3\sqrt[]{2}+\sqrt[]{2}-1-5}{2} \\ \text{midpoint}=\frac{4\sqrt[]{2}-6}{2} \\ \text{midpoint}=\frac{4\sqrt[]{2}}{2}-(6)/(2) \end{gathered}`

hence, the answer is

`\begin{gathered} \\ \text{midpoint}=2\sqrt[]{2}-3 \end{gathered}`