Help with Distance

[jinx24]

Hello again. I need a little help with this distance question. I have worked and re-worked this problem out several times and cannot figure out where I am going wrong. Thanks once again for the help.

"Give the distance from the point (1/7, -3) to the point (6/7, 1)."

d = sqrt ((X2 - X1)^2 + (Y2 - Y1)^2)
d = sqrt (( 6/7 - 1/7)^2 + (1 + 3)^2)

= sqrt(( 5/7)^2 + (4)^2)

= sqrt( 25/49 + 16)

I am stuck at this point. This question is a multiple choice one, and they way I have it so far does not look like any of the choices. Maybe I am using the wrong formula?

Here are the choices (I don't need the answer, just a way to get there!)
a) 1/7 sqrt 809
b) 1/3 sqrt 5
c) 28/5
d) 2/3 sqrt 2
e) 1/49
f) None of the above (I know this one is wrong)

Jenny

 

[Unco]

Well, 25/49 + 16 = ?

 

[jinx24]

Ok--I think I have it:

24/9 +16 = 809/49

So I now have sqrt (809/49). I am guessing that the answer is A) 1/7 sqrt 809 because the square root of 49 is 7.

Thank you! I feel so silly now! I think I just got mixed up with all of the simple adding and multiplying. I am trying to do it all without the calculator since we can't use one on our tests.

 

[Unco]

No need to guess nor use a calculator, Jenny.

\(\displaystyle \L \begin{align*}
\mbox{ \frac{25}{49} + 16 }&=\mbox{ \frac{25}{49} + \frac{16\times 49}{49} }\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&=\mbox{ \frac{25}{49} + \frac{784}{49} }\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&=\mbox{ \frac{25 + 784}{49} }\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&=\mbox{ \frac{809}{49}}
\end{align*}\)

So we have: \(\displaystyle \L \mbox{ d = \sqrt{\frac{809}{49} } = \frac{\sqrt{809 }}{\sqrt{49 }} = \frac{\sqrt{809 }}{7}}\)