# Find the value of $(a,b)$

The point $(4,1)$ is the midpoint of $(a,b)$ and $(-1,5)$.

Find the values of $a$ and $b$ considering this statement.

I know the midpoint formula is: $$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$ But I do not know how to apply it.

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Wait..... How do i do fractions!!\ –  Mark Zakhem Aug 14 at 9:12

Hints:

$$(4,1)=\left(\frac{a-1}2\;,\;\frac{b+5}2\right)\iff \begin{cases}\frac{a-1}2=4\\{}\\\frac{b+5}2=1\end{cases}$$

and now solve the easy system above...

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Nice detailed answer. Helped me out because I've got a page of these to do. I understand the concept now. THANKS! –  Mark Zakhem Aug 14 at 9:20
Any time, @MarkZakhem . Now don't forget (1) to upvote all the answers you found helpful, and after some time has ellapsed, (2) accept the answer you find the most helpful of them all. –  DonAntonio Aug 14 at 9:23
Shouldn't there be single l in elapse? –  Ramit Aug 14 at 9:27
Shouldn't there be an "a" between "be" and "single"? Just kidding...yes, apparently that word has a single "l" but I don't worry too much about that: first, english is my third langauge, and second, I'm not writing a paper or something like that. –  DonAntonio Aug 14 at 9:30

Midpoint formula is $\frac{x1 + x2}{2}$ for x, so $8 = a - 1$

$a$ is thus $9$

Similarly do $b$

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The vector from the end point you are given to the midpoint you know is $(4,1)-(-1,5)=(5,-4)$