# Thread: Unexpected turn in this pythagorean theorem equation

1. ## Unexpected turn in this pythagorean theorem equation

Hi,

I'm running into a bit of trouble with a question that requires me to calculate the distance between two points on a cartesian graph. The two points are (-5, -5.5) and (-8, 7). In the answer key of my book the equation goes (square root of)(-5-(-14))^2 + (-5.5-3)^2. That's all well and fine, but then they go: (square root of)(5+14)^2 + (-8.5)^2. The -5 in the first equation has become positive and I have no idea why. I don't think it's a typo as if I don't make this change the answer isn't plausable. Could anyone explain this one to me?

Thanks,

Kevin

2. ## Re: Unexpected turn in this pythagorean theorem equation

Are you looking at the correct answer?

The difference between -5 and -8 is 3.

The difference between -5.5 and 7 is 12.5.

The distance between the points is $\displaystyle \sqrt{3^2+12.5^2}$

3. ## Re: Unexpected turn in this pythagorean theorem equation

Hello, Kevin!

If you've typed this correctly, there is a major SNAFU in the problem.

$\displaystyle \text}Calculate the distance between }(\text{-}5, \text{-}5.5)\text{ and }(\text{-}8, 7).$

$\displaystyle \text{In my book, the equation goes: }\:\sqrt{\big(\text{-}5-[{\color{red}\text{-}14}]\big)^2 + \big(\text{-}5.5 -{\color{red}3}\big)^2}\quad {\color{blue}What?}$

$\displaystyle \text{That is the distance between }(\text{-}5,\text{-}5.5)\text{ and }{\color{red}(\text{-}14, 3)}.$

$\displaystyle \text{And there is }no\;way\text{ that -}5\text{ could suddenly become +}5.$

4. ## Re: Unexpected turn in this pythagorean theorem equation

Sorry guys, typed in the wrong coordinates in my OP. Its supposed to be (-5, 5.5) (-14, 3). I'm actually supposed to find the length of two line segments, from (-5, -5.5) (-14, 3) and from (-5, -5.5) (-8, 7). Still, the answer key shows sqrt[(-5-(-14)2 + (-5.5-7)2] as sqrt[19^2 + -8.5^2]. The wierd thing is that when I plug in the coordinates into sqrt[[(-5-(-8))2 + (-5.5-7)2 ] and sqrt[(-5-(-14)2 + (-5.5-7)2] I get very similar numbers, even though their spacing apart from each other on the graph suggests I should get a bigger one.

5. ## Re: Unexpected turn in this pythagorean theorem equation

Originally Posted by KevinShaughnessy
Sorry guys, typed in the wrong coordinates in my OP. Its supposed to be (-5, 5.5) (-14, 3). I'm actually supposed to find the length of two line segments, from (-5, -5.5) (-14, 3) and from (-5, -5.5) (-8, 7). Still, the answer key shows sqrt[(-5-(-14)2 + (-5.5-7)2] as sqrt[19^2 + -8.5^2].
This is still wrong. -5.5-7= -12.7, not -8.5. You seem to be a little careless with negatives signs.

The wierd thing is that when I plug in the coordinates into sqrt[[(-5-(-8))2 + (-5.5-7)2 ] and sqrt[(-5-(-14)2 + (-5.5-7)2] I get very similar numbers, even though their spacing apart from each other on the graph suggests I should get a bigger one.
$\displaystyle \sqrt{(-5-(-8))^2+ (-5.5-7)^2}=\sqrt{3^2+ (-12.7)^2}= \sqrt{161.29}= 12.7$
Is that what you get?

$\displaystyle \sqrt{(-5-(-14))^2+ (-5.5-7)^2}= \sqrt{9^2+ (-12.7)^2}= \sqrt{242.29}= 15.7$
Is that what you get?

6. ## Re: Unexpected turn in this pythagorean theorem equation

I am being careless, I'm sorry. I appreciate your patience. I meant to type sqrt[(-5-(-14)2 + (-5.5-3)2] = sqrt[19^2 + -8.5^2]. The answers I get as the distances of the line segments are 12.38 and 12.85. My concern was that that seemed too similar based on an eyeballing of the graph, but when I measured with a ruler I found it to be accurate. I'm going to chalk this one up as a typo in the book, which is a safe bet based on the physical measurements of the distances.

Thanks alot for your help guys!