Trouble with basic Vector Addition Problem

[ERoday]

This a book example that I have the answer to but do not understand.
What are the magnitude and direction of the total displacement for the treasure hunt? The instructions to find the treasure are 5 paces North, 3 paces East, then 4 paces Southeast. Each pace is 0.750 m in length.

So I understand that to find the total displacement you need to find the components of each vector. So 5 pace North = vector [A] which would be Ax= 0 and Ay= 3.75m, and 3 paces east =vector which would be Bx= 2.25m and By= 0 but for 4 paces southeast the book gives the answer to be Cx=2.12 and Cy =-2.12 and I understand why those components are positive and negative but not why the distance is 2.12. Why isn't it Cx=3.00m and Cy= -3.00m?

 

[vela]

What would the length of the vector C be if C_x and C_y were both 3.00 m?

 

[ERoday]

[4.24m] so bad logic on my part but I still don't understand how to find vector [C]

 

[ehild]

I hope you understand the problem easier from a drawing. All length are in paces. Find the x, y components of the red vector (in paces) first.

ehild.

 

[vela]

You want the length of C to be 3.00 m. Since you're going southeast, you know that C_y = -C_x. Put those two statements together to solve for C_x and C_y.

 

[ERoday]

I understand it better now. Thanks. I see that vector [C] is a hypotenuse type angle (forgive my serious lack of physics jargon) so I can look at the intersection and see that the angle is 45 degrees and use sine and cosine to find Cx and Cy. I just thought there was a simpler way to do it. Like for vectors [A] and I just looked at the positive and negative positions to find the components.