Question

If $P(\frac{a}{3},\frac{b}{2})$ is the mid-point of the line segment joining $A(-4,3)$ and $B(-2,4)$, then $(a,b)$ is

• A. $(-9,7)$
• B. $(-3,\frac{7}{2})$
• C. $(9,-7)$
• D. $(3,-\frac{7}{2})$

Answer 1

The correct option is A $(-9,7)$

Using the midpoint formula, $(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ where $x_1=-4$,$y_1=3$,$x_2=-2$, $y_2=4$

Given $P$ is a mid-point of $AB$

$\Rightarrow P(\frac{a}{3},\frac{b}{2})=(\frac{-4-2}{2},\frac{3+4}{2})=(-3,\frac{7}{2})$

Equating the $x$ and $y$ coordinates, we get

$\Rightarrow \frac{a}{3}=-3,\frac{b}{2}=\frac{7}{2}$

$\Rightarrow a=-9,b=7$

$\therefore (a,b)=(-9,7)$