Calculus and vectors

Vector AB is a vector whose tail is at (-4,2) and whose head is at (-1,3).
Calculate the magnitude of vector AB
Determine the coordinates of point D on vector CD, if C (-6,0) and vector CD= vector AB.

Please I need some help. Is there a formula to solve this? Pls help

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  1. I will let A be (-4,2) and B(-1,3)
    vector AB = ( -1+4 , 3-2)
    = (3,1)
    magnitude of AB = √(3^2 + 1^2) = √10

    let D be (x,y)
    the vector CD = (x+6, x-0) = (x+6 , y)
    but if vector AB = vector CD
    then x+6 = 3
    x = -3
    and y = 1
    so point D is (-3,1)

    in general if A is the point (a,b) and B is the point (c,d)
    then vector AB = ( c-a , d-b)
    and vector BA = ( a - c, b - d)

    note that vector AB = - vector BA

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  2. Very well explained thank you.

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