Question

Given point $A(-3,-8)$, if the midpoint of segment $AB$ is $(1,-5)$, calculate the coordinates of point $B$.

• A. $(5,-2)$
• B. $(4,-2)$
• C. $(-1,-6.5)$
• D. $(-2,-2)$

Answer 1

The correct option is A $(5,-2)$

Given, coordinates $A(-3,-8)$ and the mid point of $AB$ is $(1,-5)$

As per Midpoint formula coordinates of mid point $=$ $\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$

Let the coordinates of point $B$ be $(x,y)$

Then $(1,-5)=[\left(\frac{-3+x}{2}\right),\left(\frac{-8+y}{2}\right)]$

Then $\frac{-3+x}{2}=1$

$\Rightarrow -3+x=2$

$\Rightarrow x=2+3=5$

Then$\frac{-8+y}{2}=-5$

$\Rightarrow -8+y=-10$

$\Rightarrow y=-10+8=-2$

Then coordinates of $B$ is $(5,-2)$.