Question

Point M is the midpoint of segment AB. If the coordinates of Mare (2, 8) and the coordinates of Aare (10, 12), find the coordinates of B.B(x, y) =(

Answer 1

Using the formula

`(x_{m\text{ , }}y_m)\text{ = (}(x_1+x_2)/(2)\text{ , }(y_1+y_2)/(2))`

x₁= 10 y₁=12 Xm=2 Ym = 8

x₂ = ? y₂=?

Substituting and solving for x₂

`x_m=(x_1+x_2)/(2)`

`2\text{ = }(10+x_2)/(2)`

Multiply both-side of the equation by 2

4 = 10 + x₂

subtract 10 from both-side of the equation

-6 = x₂

x₂= -6

Similarly, substituting and solving for y₂

`y_m=(y_1+y_2)/(2)`

`8=(12+y_2)/(2)`

Multiply both-side of the equation by 2

16 = 12 + y₂

Subtract 12 from both-side of the equation

4 = y₂

y₂= 2

Hence; coordinates of B are;

B(x,y) = ( -6, 2)