Question

The coordinates of the midpoint of line segment AB are $(1,-2)$, if the coordinates of A are $(-3,2)$ then the coordinates of B are:

• A. $(3,-5)$
• B. $(5,-6)$
• C. $(4,-2)$
• D. $(5,-4)$

Answer 1

The correct option is B $(5,-6)$

Given that, the coordinates of the midpoint of line segment $AB$ are $(1,-2)$. Also, coordinates of $A$ are $(-3,2)$.

To find out: Coordinates of $B$.

Let the coordinates of $B$ be $(a,b)$
We know that,
Midpoint of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
Hence, midpoint of $AB=(\frac{-3+a}{2},\frac{2+b}{2})=(1,-2)$
$\Rightarrow \frac{-3+a}{2}=1;\frac{2+b}{2}=-2$
$\Rightarrow -3+a=2;2+b=-4$
$\therefore a=5;b=-6$

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