Question

The midpoint of AB is M (5, 6). If the coordinates of A are (3, 8), what are the

Answer 1

Answer:

(7, 4)

Step-by-step explanation:

$\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}$

By the midpoint formula,
$(x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )$

$x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2}$

We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
$5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7$

$6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4$

So coordinates of B are (7,4)