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

Substituting the values of $x$ and $y$ in the given options.
$\begin{array}{cc}6x+y& =6\times \frac{3}{2}+(-1)\\ & =9-1\\ & =8\end{array}$

So, the values of $x$ and $y$ are true for the equation $6x+y=8$.

Thus, 6x + y = 8