Question

The mid-point of the line segment $AB$ where cordinates of $A$ are $(-2,\frac{x}{2})$ and coordinates of B are $(\frac{x}{4},2)$ is

• A. $(-\frac{x}{8},\frac{x}{4})$
• B. $(1+\frac{x}{8},1+\frac{x}{8})$
• C. $(-1+\frac{x}{8},1+\frac{x}{4})$
• D. $(1+\frac{x}{4},1-\frac{x}{4})$

Answer 1

The correct option is C

$(-1+\frac{x}{8},1+\frac{x}{4})$

Let the mid-point of the line segment $AB$ be $(a,b)$.

Given, cordinates of $A$ are $(-2,\frac{x}{2})$ and coordinates of B are $(\frac{x}{4},2)$.

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, $a=\frac{-2+\frac{x}{4}}{2}=\frac{-8+x}{8}=-1+\frac{x}{8}$

Also, $b=\frac{\frac{x}{2}+2}{2}=\frac{x+4}{4}=1+\frac{x}{4}$

The coordinates of the required mid-point are $(-1+\frac{x}{8},1+\frac{x}{4})$