Question

If the co-ordinates of middle point of line segment joining ( 2 , 1 ) and ( 1 , -3 ) are Csf%7B%28%20%5Calpha%20%5C%3A%2C%20%5C%3A%20%5Cbeta%20%29%20%7D" id="TexFormula1" title=" \sf{( \alpha \:, \: \beta ) }" alt=" \sf{( \alpha \:, \: \beta ) }" align="absmiddle" class="latex-formula"> , prove that $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$

Answer 1

Answer:

α=

2

2+1

=

2

3

β=

2

1+(−3)

=

2

−2

=−1

Substitute the values in given equation:

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

2

3

)+(−1)−8

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

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

Answer 2

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 $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$