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 $y=-1$.