The midpoint of AB is (3,7). The coordinate of one endpoint is A(5,1). Find the coordinate of endpoint B. Show or explain work.

Question

The midpoint of AB is (3,7). The coordinate of one endpoint is A(5,1). Find the coordinate of endpoint B. Show or explain work.

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    0
    2021-11-25T22:31:41+00:00

    We have a line AB with point P
    A(5,1) which becomes (x1,y1)
    P(3,7) which becomes (x,y)
    B(x,y) which becomes (x2,y2)

    Since it is a midpoint, we can use the midpoint formula directly.

    x = (x1+x2)/2

    3 = (5+x)/2
    x=1
    Thus our x coordinate is 1

    y = (y1+y2)/2

    7 = (1+y)/2
    y=13
    Thus our y coordinate is 13

    Our answer is B(1,13)

    0
    2021-11-25T22:31:46+00:00

    The formula of a midpoint:

    M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)

    We have

    M(3,\ 7)\to x_M=3,\ y_M=7\\\\A(5,\ 1)\to x_A=3,\ y_A=7

    Substitute:

    \dfrac{5+x_B}{2}=3\qquad|\cdot2\\\\5+x_B=6\qquad|-5\\\\x_B=1\\\\\dfrac{1+y_B}{2}=7\qquad|\cdot2\\\\1+y_B=14\qquad|-1\\\\y_B=13

    Answer: B(1, 13)

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