- Let (X1, Y1) be one end point of the line segment that represents (1,2).
- Let (Xm, Ym) be the coordinates of the midpoint of the line segment which are given as (-1,4).
- Let (X2, Y2) be the other end point which has to be found out.
It then can be stated:
[tex]\large\red\hookrightarrow \rm \large \: \:X_m \: = \: \frac{X_1 \: + \: \: X_2 }{2} \: \: \: \: \: \: \: \:... (1) \\ [/tex]
[tex]\large\red\hookrightarrow \rm \large \: \:Y_m \: = \: \frac{Y_1 \: + \: \: Y_2 }{2} \: \: \: \: \: \: \: \:... (2)\\ [/tex]
Since, Xm = -1 and X1 = 1 we can write equation (1) as
[tex]\large\purple\longrightarrow \rm \large \: \:-1 \: = \: \frac{1 \: + \: \: X_2 }{2} \: \: \: \: \: \: \: \:... (1) \\ [/tex]
[tex]\large\purple\longrightarrow \rm \large \: \:-2 \: = \:1 \: + \: X_2[/tex]
[tex]\large\purple\longrightarrow \rm \large \: \: - 2 \: - 1 \: = \: X_2[/tex]
[tex]\large\purple\longrightarrow \rm \large \: \: - 3 \: = \: X_2[/tex]
Since , Ym = 4 and Y1 = 2 we can write the equation (2) as
[tex]\large\purple\longrightarrow \rm \large \: \:4 \: = \: \frac{2 \: + \: \: Y_2 }{2} \: \: \: \: \: \: \: \:... (2)\\ [/tex]
[tex]\large\purple\longrightarrow \rm \large \: \:8 \: = \: 2 \: + \: Y_2[/tex]
[tex]\large\purple\longrightarrow \rm \large \: \:8 \: - \: 2 \: = \: Y_2[/tex]
[tex]\large\purple\longrightarrow \rm \large \: \:6 \: = \: Y_2[/tex]
Therefore the other endpoint of the line (X2, Y2) is (-3 , 6)
