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)?

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Answer 1 · 2017-05-20T20:28:47

See a solution process below:

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

$M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)$

Where $M$ $M$ 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: $(color(blue)(6.5), color(blue)(15))$