Question

The midpoint of the line segment joining $(A,3)$ and $(4,B)$ is $(3,5)$. What are the values of $A$ and $B$?

• A. $A=2,B=2$
• B. $A=7,B=7$
• C. $A=7,B=2$
• D. $A=2,B=7$

Answer 1

The correct option is D $A=2,B=7$

Midpoint of two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Here, $x_1=A,x_2=4,y_1=3$ and $y_2=B$. Coordinates of midpoint is $(3,5)$. Equating them:

$\frac{A+4}{2}=3$
$A+4=6$
$A=2$

$\frac{3+B}{2}=5$
$3+B=10$
$B=7$