A line segment has an endpoint at (3, 2). If the midpoint of the line segment is (6, -2), what are the coordinates of the point at the other end of the line segment?

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Answer 1 · 2017-06-13T07:06:45

The other endpoint is #(9,-6)#

Substitute the given values into the formula for midpoint:

#color(red)((x_1,y_1) = (3,2)) and color(blue)(M=(6,-2))#

#(color(red)(x_1)+x_2)/2 = color(blue)(x) " "and" "(color(red)(y_1)+y_2)/2= color(blue)(y) #

#(color(red)(3)+x_2)/2 = color(blue)(6) " "and" "(color(red)(2)+y_2)/2= color(blue)(-2) " "larr xx 2#

#color(red)(3)+x_2 = color(blue)(12) " "and" "color(red)(2)+y_2= color(blue)(-4) #

#x_2 =9" "and" "y_2=-6#

The other endpoint is #(9,-6)#