Question

The Coordinates of the endpoints of a line segments are (3,1) and (-5, 9). Find the coordinates of the midpoint of the line segment

a. 4,5
b. -1,5
c. -2, 4
d. -2, 8

Answer 1

The coordinates of the midpoint are the arithmetic means of the respective coordinates of the endpoints.


`(3,1) \\ x_1=3 \\ y_1=1 \\ \\ (-5,9) \\ x_2=-5 \\ y_2=9 \\ \\ \hbox{the x-coordinate of the midpoint:} \\ (x_1+x_2)/(2)=(3-5)/(2)=(-2)/(2)=-1 \\ \\ \hbox{the y-coordinate of the midpoint:} \\ (y_1+y_2)/(2)=(1+9)/(2)=(10)/(2)=5`

The coordinates of the midpoint are B. (-1,5).