Question

Point A is located at (3,6). The midpoint of line segment AB is point C(11,13). What are the coordinates of point B? Use the midpoint formula and show ALL work. DO NOT use Desmos.

Answer 1

Answer: The coordinates of point B are (19 , 20).

Explanation:

The mid point (x,y) of line joining (a,b) and (c,d) is given by :-

`(x,y)=((a+c)/(2),(b+d)/(2))` (1)

Given : Point A is located at (3,6). The midpoint of line segment AB is point C(11,13).

Let the coordinates of point B are (a,b) m, the according to (1) , we have

`((3+a)/(2),(6+b)/(2))=(11,13)\\\\\Rightarrow\ (3+a)/(2)=11\ \ ,\ \ (6+b)/(2)=13\\\\\Rightarrow\ 3+a=22\ \ ,\ \ \ 6+b=26\\\\\Rightarrow\ a=19,\ \ b= 20`

Hence, the coordinates of point B are (19 , 20).