Question

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

Answer 1

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

Let the coordinates of `color(red)(S)` be `color(red)("("x_s,y_s")")`

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

`(y " at "color(blue)(R)) - (y " at "color(green)(T)) =(y " at " color(green)(T)) - (y " at " color(red)(S))`
That is
`color(blue)(7)-color(green)(4) = color(green)(4)-color(red)(y_s)`
`rarr color(red)(y_s) =1`

Similarly for `color(red)(x_s)`
`color(blue)(9)-color(green)(5) = color(green)(5)-color(red)(x_s)`
`rarr color(red)(x_s)=1`

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