Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)

Answer :

Answer:

[tex](2x_m - x_1 , 2y_m -y_1)[/tex]

Step-by-step explanation:

Let [tex](x,y)[/tex] be the unknown endpoint.

Denote the one endpoint by [tex](x_1, y_1)[/tex] and the midpoint by [tex](x_m, y_m)[/tex].

As the midpoint divides the segment in [tex]1:1[/tex] ratio, so, from section formula

[tex]x_m=\frac{x_1+x}{2} \Rightarrow x=2x_m-x_1.[/tex]

and [tex]y_m=\frac{y_1+x}{2} \Rightarrow y=2x_m-y_1.[/tex]

Hence, the coordinate of the other endpoint is [tex](x,y)=(2x_m - x_1 , 2y_m -y_1)[/tex].

Other Questions