Question

The midpoint of a line segment is (2, -1) and one endpoint of the segment is (-1, -3). Find the coordinates of the other segment.

Answer 1

Given:

The midpoint of line segment is (2,-1).

One end point is (-1,-3).

Let, the other endpoint be (x,y)

The midpoint of the line segment is calculated as,

`\begin{gathered} M=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ (x_1,y_1)=(-1,-3),(x_2,y_2)=(x,y),M=(2,-1) \\ (2,-1)=((-1+x)/(2),(-3+y)/(2)) \\ \Rightarrow(-1+x)/(2)=2,(-3+y)/(2)=-1 \\ -1+x=4,-3+y=-2 \\ x=4+1,y=-2+3 \\ x=5,y=1 \end{gathered}`

Answer: the coordinates of the other endpoint of the line segment is (5,1)