Question

The line AB had midpoint (2, 5).A has coordinates (1, 2).Find the coordinates of B.

Answer 1

Answer:

The line AB, with A(Ax, Ay), B(Bx, By) and midpoint M(Mx, My) satisfying:

Ax + Bx = 2Mx

Ay + By = 2My

=>

2 + Bx = 2*1

5 + By = 2*2

=> Bx = 0

=> By = -1

=> B(0, -1)

Hope this helps!

:)

Answer 2

Answer:

B(3, 8 )

Step-by-step explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ $\frac{1}{2}$(x₁ + x₂ ), $\frac{1}{2}$(y₁ + y₂ ) ]

let the coordinates of B = (x, y ), then

$\frac{1}{2}$(1 + x) = 2 ( multiply both sides by 2 )

1 + x = 4 ( subtract 1 from both sides )

x = 3

and

$\frac{1}{2}$ (2 + y) = 5 ( multiply both sides by 2 )

2 + y = 10 ( subtract 2 from both sides )

y = 8

Thus

coordinates of B = (3, 8 )