Question

If the co-ordinates of middle point of line segment joining ( 2 , 1 ) and ( 1 , -3 ) are $\sf{( \alpha \:, \: \beta ) }$ , prove that $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$

Answer 1

By the midpoint formula,

$\alpha = \frac{2+1}{2}=\frac{3}{2}\\

\beta =\frac{1+(-3)}{2} = \frac{-2}{2} = -1$

Substitute the values in given equation:

$\text{LHS} = 6 \Big( \frac{3}{2}\Big) + (-1)-8$

$\implies \text{LHS}= 9-1 -8 =0 =\text{RHS}$

Since both sides are equal, this proves the equation $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$