Geometry Help! Vecotor? Magnitude?

Question

I am really struggling with this! There are 3 parts to these question so please make sure you read carefully!

Q1.: Given points A(-7,6) and B(2,3) Sketch Vector AB on the graph.
(I DID SO)!!

Q2: Find Vector AB in Problem above as an ordered pair.
AB=Change in X, Change in Y
I put: Change in x= 2-(-7)= 9
Change in y=3-6= -3
So therefor I got the Vector of AB= (9,-3)

Q3: Find the magnitude of Vector AB in problem above. Leave in simplest radical form.
I used the pythagorean Theorem and I put:
9^2 + -3^2= 90
(9*9=81) +(-3*(-3)= 9=90 ^2= squared!!

Is this in simplest form?? Also is this correct? If not, can you please explain to me step by step how to work this problem out! Thanks in advance!! ALSO, how do you get the simplest form?

Answer 1

Q3: c^2 = 90 so C = square root of 90. That simplifies to 3* square root of 10.

Answer 2

You've mostly got it. Your answer to #3 is wrong because you forgot to square-root the whole thing. The magnitude is actually the square root of 90, which in simplest form is 3 times the square root of 10.

Here's why you square-root it: The magnitude of a vector is just its length. So you're trying to find the length of the line between the points (0,0) and (9,-3), which is the same as the length of the vector between them. The way to find the length of a diagonal line like that is to draw in the horizontal and vertical lines to turn it into a right triangle, and then use the Pythagorean theorem. That's what you're doing.