Question

The midpoint of line segment AB is $(2,-5)$. If the coordinates of point A are $(4,4)$, what are the coordinates of B?

• A. $(3,\frac{9}{2})$
• B. $(0,14)$
• C. $(3,-\frac{9}{2})$
• D. $(0,-14)$

Answer 1

The correct option is D

$(0,-14)$

Given that $(2,-5)$ is the mid-point of the line segment AB where coordinates of point A are $(4,4)$.

Let the coordinates of point B be $(x_2,y_2)$.

We know that mid-point of the line joining two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

$\Rightarrow x_2=0$

Also, $\frac{4+y_2}{2}=-5$
$\Rightarrow y_2=-14$
Therefore coordinates of point B are $(0,-14)$