Question

How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5,-6) and the midpoint M(1.5,4.5)?

Answer 1

See a solution process below:

Explanation:

The formula to find the mid-point of a line segment give the two end points is:

`M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)`

Where `M` is the midpoint and the given points are:

`(color(red)((x_1, y_1)))` and `(color(blue)((x_2, y_2)))`

Substituting the information we have gives:

`(1.5, 4.5) = ((color(red)(-3.5) + color(blue)(x_2))/2 , (color(red)(-6) + color(blue)(y_2))/2)`

To find `color(blue)(x_2)` we need to solve this equation:

`1.5 = (color(red)(-3.5) + color(blue)(x_2))/2`

`color(green)(2) xx 1.5 = color(green)(2) xx (color(red)(-3.5) + color(blue)(x_2))/2`

`3 = cancel(color(green)(2)) xx (color(red)(-3.5) + color(blue)(x_2))/color(green)(cancel(color(black)(2)))`

`3 = color(red)(-3.5) + color(blue)(x_2)`

`3.5 + 3 = 3.5 color(red)(- 3.5) + color(blue)(x_2)`

`6.5 = 0 + color(blue)(x_2)`

`6.5 = color(blue)(x_2)`

`color(blue)(x_2) = 6.5`

To find `color(blue)(y_2)` we need to solve this equation:

`4.5 = (color(red)(-6) + color(blue)(y_2))/2`

`color(green)(2) xx 4.5 = color(green)(2) xx (color(red)(-6) + color(blue)(y_2))/2`

`9 = cancel(color(green)(2)) xx (color(red)(-6) + color(blue)(y_2))/color(green)(cancel(color(black)(2)))`

`9 = color(red)(-6) + color(blue)(y_2)`

`9 + 6 = 6 color(red)(- 6) + color(blue)(y_2)`

`15 = 0 + color(blue)(y_2)`

`15 = color(blue)(y_2)`

`color(blue)(y_2) = 15`

The other end point of the segment is: `(color(blue)(6.5), color(blue)(15))`