Question

M(5a, 9) is the mid-point of A(4, 10) and B(2a, 8), then the value of a is:​

Answer 1

Answer:

here, (4+2a)/2=5a

=> 2(2+a)/2=5a

=> 2+a=5a

=> 5a-a=2

=> 4a=2

=> a=2/4

=> a=1/2

value of a=1/2

Answer 2

SOLUTION

GIVEN

M(5a, 9) is the mid-point of A(4, 10) and B(2a, 8)

TO DETERMINE

The value of a

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The midpoint of the line AB is

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} \bigg)}$

EVALUATION

Here it is given that M(5a, 9) is the mid-point of A(4, 10) and B(2a, 8)

The mid-point of A(4, 10) and B(2a, 8)

$\displaystyle \sf{ = \bigg( \frac{4 + 2a}{2} , \frac{10 + 8}{2} \bigg)}$

$\displaystyle \sf{ = ( 2 + a, 9 )}$

So by the given condition

2 + a = 5a

$\displaystyle \sf{ \implies 5a - a = 2}$

$\displaystyle \sf{ \implies 4a = 2}$

$\displaystyle \sf{ \implies a = \frac{1}{2} }$

FINAL ANSWER

Hence the required value of

$\displaystyle \sf{ a = \frac{1}{2} }$

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