Question

Point M is the midpoint of AB if the coordinates of A are (-3,6) and the coordinates of M are (-5,2) what are the coordinates of B ?
Please answer #5

Answer 1

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 $x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}$

∵ 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

∵ $-5=\frac{-3+x_{2}}{2}$ ⇒ multiply both sides by 2

∴ $-10=-3+x_{2}$ ⇒ add 3 to both sides

∴ -7 = x2

∵ $2=\frac{6+y_{2}}{2}$ ⇒ multiply both sides by 2

∴ $4=6+y_{2}$ ⇒ subtract 6 from both sides

∴ -2 = y2

∵ The coordinates of point B are (x2 , y2)

∴ The coordinates of point B are (-7 , -2)