Question

If $M(4,5)$ is the mid-point of the line segment $AB$ and co-ordinates of $A$ are $(3,4)$, then find the co-ordinates of point $B$.

Answer 1

$M(4,5)$ is mid-point of $AB$ where $A(3,4)$ and the coordinates of $B$ are $(x_2,y_2)$.

Coordinates of mid-point of two points with coordinates $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula:

$(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$\therefore (4,5)=(\frac{3+x_2}{2},\frac{4+y_2}{2})$

On comparing the coordinates:

$\frac{3+x_2}{2}=4$

$x_2+3=8$

$⟹x_2=5$

$\frac{4+y_2}{2}=5$

$y_2+4=10$

$⟹y_2=6$

Hence, coordinates of $B$ are $(5,6)$.