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

##### 1 Answer

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

#### Explanation:

We have

So in vector notation we can write:

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

We can calculate

**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

**Method 2:**

Using vector notation we can calculate the vector

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.