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 = (2+1)/(2)=(3)/(2)\\</p><p>\beta =(1+(-3))/(2) = (-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 $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$