If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.

Question

If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.

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Ngọc Khuê 5 months 2021-08-06T15:43:01+00:00 1 Answers 10 views 0

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    2021-08-06T15:44:34+00:00

    Answer:

    Step-by-step explanation:

    The formula to find the midpoint of a segment is

    M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) and we have the midpoint and we also have a coordinate of (5, 4). Let’s let x₁ = 5 and y₁ = 4. Filling in what we have:

    (2,1)=(\frac{5+x_1}{2},\frac{4+y_2}{2}) and we’ll deal with the x terms first. The x coordinate of the midpoint is 2, so:

    2=\frac{5+x_2}{2} and multiply both sides by 2 to get rid of the denominator to get:

    4 = 5 + x₂ so

    x₂ = -1. Going on to the y coordinate. The y coordinate of the midpoint is 1, so:

    1=\frac{4+y_2}{2} and again multiply both sides by 2 to get rid of the denominator to get:

    2 = 4 + y₂ so

    y₂ = -2

    The coordinates of T are (-1, -2)

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