How do you find the magnitude of YZ given Y(5,0) and Z(7,6)?

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Answer 1 · 2017-09-15T00:47:03

$bb(vec(YZ)) = ( (2), (6) ) \ \$ and $\ \ abs(bb(vec(YZ))) = 2sqrt(10)$

We have $Y$ and $Z$ with coordinates $(5,0)$ and $(7,6)$ respectively.

So in vector notation we can write:

$bb(vec(OY)) = ( (5), (0) ) \ \$ and $\ \ bb(vec(OZ)) = ( (7), (6) )$

We can calculate $abs(bb(vec(YZ)))$ in several ways:

Method 1:

Using the coordinates along, we can apply pythagoras theorem:

$YZ^2 = (7-5)^2 + (6-0)^2$
$\ \ \ \ \ \ \ = 2^2 + 6^2$
$\ \ \ \ \ \ \ = 4+36$
$\ \ \ \ \ \ \ = 40$

And so $YZ = sqrt(40) = 2sqrt(10)$

Method 2:

Using vector notation we can calculate the vector $bb(vec(YZ))$ and then calculate its magnitude.

We have:

$bb(vec(YZ)) = bb(vec(OZ)) - bb(vec(OY))$
$\ \ \ \ \ \ = ( (7), (6) ) - ( (5), (0) )$
$\ \ \ \ \ \ = ( (7-5), (6-0) )$
$\ \ \ \ \ \ = ( (2), (6) )$

And so:

$abs(bb(vec(YZ))) = sqrt(2^2+6^2)$
$\ \ \ \ \ \ \ \ = 2sqrt(10)$ , as before.