Question

The midpoint of the line joining (a, -b) and (3a, 5b) is _______.
A)(-a, 2b)
B)(2a, 4b)
C)(2a, 2b)
D)(-a, 3b)...

Answer 1

$The \:mid\: point \: M(x,y) \:of \:the \:line \\segment \: joining \: the \: points \:(x_{1} , y_{1})\\and \: (x_{2} , y_{2})$

$\pink { M(x,y) = \Big( \frac{x_{1} + x_{2}}{2} , \frac{y_{1} + y_{2}}{2} \Big)}$

$\therefore The \:mid \:point \: of \: the \:line \\segment \: joining \: the \: points \\(a,-b) \: and \:(3a,5b) \:is$

$M(x,y) = \Big (\frac{a+3a}{2} , \frac{-b+5b}{2}\Big)$

$= \Big( \frac{4a}{2} , \frac{4b}{2}\Big) \\= ( 2a,2b)$

Therefore.,

$Option \: \green { ( C) } \:is \: correct$

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