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

1 Answer
Sep 15, 2017

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

Explanation:

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.