Question

If the coordinates of the mid-point of the line segment joining the points $(2,1)$ and $(1,-3)$ is $(x,y)$. What is the relation between $x$ and $y$?

• A. 6x + y = 8
• B. 2x - 5y = 4
• C. 3x - y = 5
• D. 2x + 1 = 0

Answer 1

The correct option is A

6x + y = 8

From the section formula if $(x,y)$ are the midpoints of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$,

then $x=\frac{x_1+x_2}{2}$ and

$y=\frac{y_1+y_2}{2}$.

So $x=\frac{3}{2}$ and $y=-1$.

Among the equations given, just the first equation i.e. $6x+y=8$ satisfies the value of​ $x=\frac{3}{2}$ and $y=-1$.