The midpoint of segment AB is (6. 5). The coordinates of point A are (7, 10). How do you find the coordinates of point B?

Dec 30, 2016

$\therefore B \left(7 , 0\right)$

Explanation:

Substitute the values into the formula for the midpoint:

x co-ordinate: $x = \frac{{x}_{A} + {x}_{B}}{2}$ and y co-ordinate: $y = \frac{{y}_{A} + {y}_{B}}{2}$

$6 = \frac{7 + {x}_{B}}{2} \text{ }$ and $\text{ } 5 = \frac{10 + {y}_{B}}{2}$

$12 = 7 + {x}_{B} \text{ }$ and $\text{ } 10 = 10 + {y}_{B}$

$12 - 5 = {x}_{B} \text{ }$ and $\text{ } 10 - 10 = {y}_{B}$

$7 = {x}_{B} \text{ }$ and $\text{ } 0 = {y}_{B}$

$\therefore B \left(7 , 0\right)$