SOLUTION: For the Initial point of (1,11) and the Terminal point of (9,3), how would you find the component and magnitude?

Algebra ->  Vectors -> SOLUTION: For the Initial point of (1,11) and the Terminal point of (9,3), how would you find the component and magnitude?       Log On


   

Question 1060048: For the Initial point of (1,11) and the Terminal point of (9,3), how would you find the component and magnitude?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Subtract the x coordinates (terminal - initial) to get
9-1 = 8

Do the same for the y coordinates
3-11 = -8

So the component form of this vector is < 8, -8 >

Let's find the magnitude now. We'll use this formula
d = sqrt(a^2 + b^2)
where "sqrt" stands for "square root"

In this case, a = 8 and b = -8, so

d = sqrt(a^2 + b^2)
d = sqrt(8^2 + (-8)^2)
d = sqrt(128)
d = sqrt(64*2)
d = sqrt(64)*sqrt(2)
d = 8*sqrt(2) exact form
d = 11.3137084989848 approximate form

The exact magnitude is 8*sqrt(2)

while the approximate magnitude is 11.3137084989848