Answer:
The coordinates of point B are (-7 , -2)
Step-by-step explanation:
* Lets explain how to solve the problem
- The mid-point (x , y) of the line whose endpoints are (x1 , y1) and
(x2 , y2) is [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ M is the midpoint of AB
∵ The coordinates of point A are (-3 , 6)
∵ The coordinates of point M are (-5 , 2)
- Let the coordinates of point A are (x1 , y1) , The coordinates of
point B are (x2 , y2) and The coordinates of point M are (x , y)
∴ x = -5 , x1 = -3 and y = 2 , y1 = 6
- Lets use the rule of the mid point to find x2 , y2
∵ [tex]-5=\frac{-3+x_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]-10=-3+x_{2}[/tex] ⇒ add 3 to both sides
∴ -7 = x2
∵ [tex]2=\frac{6+y_{2}}{2}[/tex] ⇒ multiply both sides by 2
∴ [tex]4=6+y_{2}[/tex] ⇒ subtract 6 from both sides
∴ -2 = y2
∵ The coordinates of point B are (x2 , y2)
∴ The coordinates of point B are (-7 , -2)
