What are the coordinates of S, if the midpoint of s (5, 4) and the coordinates of R are (9, 7)?

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What are the coordinates of S, if the midpoint of s (5, 4) and the coordinates of R are (9, 7)?

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Answer 1 · 2015-05-06T11:38:47

$S R$ $color(red)(S)color(blue)(R)$ is a line segment with $R$ $color(blue)(R)$ at $(9, 7)$ $color(blue)("("9,7")")$ and the midpoint of $color(red(S)color(blue)(R)$ (let's call it $T$ $color(green)(T)$ ) at $(5, 4)$ $color(green)("("5,4")")$

Let the coordinates of $S$ $color(red)(S)$ be $(x_{s}, y_{s})$ $color(red)("("x_s,y_s")")$

Since $T$ $color(green)(T)$ is the midpoint of $S R$ $color(red)(S)color(blue)(R)$

$(y at R) - (y at T) = (y at T) - (y at S)$ $(y " at "color(blue)(R)) - (y " at "color(green)(T)) =(y " at " color(green)(T)) - (y " at " color(red)(S))$
That is
$7 - 4 = 4 - y_{s}$ $color(blue)(7)-color(green)(4) = color(green)(4)-color(red)(y_s)$
$\to y_{s} = 1$ $rarr color(red)(y_s) =1$

Similarly for $x_{s}$ $color(red)(x_s)$
$9 - 5 = 5 - x_{s}$ $color(blue)(9)-color(green)(5) = color(green)(5)-color(red)(x_s)$
$\to x_{s} = 1$ $rarr color(red)(x_s)=1$

The coordinates of $S$ $color(red)(S)$ are $(1, 1)$ $color(red)("("1,1")")$

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What are the coordinates of S, if the midpoint of s (5, 4) and the coordinates of R are (9, 7)?

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