Question

P (1, 1) is midpoint of segment joining A (a, 0) and B (0, b)

show that

1
/a+
1
/b
= 1

​

Answer 1

Correct question :

P (1, 1) is midpoint of line segment joining A (a, 0) and B (0, b). Show that (1/a)+(1/b) = 1

Solution :

$\rm \: Coordinate \: of \: point \: passing \: through \: midpoint \: of \: line \: segment \: joining\: points \: (x_1 , y_1) \: and \: (x_2 , y_2) : \\ \\ { \bigg( \rm \: \dfrac{x_1 +x_2 }{2} }, \rm\dfrac{y_1 +y_2 }{2}\bigg)$

$\rm \longrightarrow \: (1,1) = { \bigg( \rm \: \dfrac{a +0}{2} }, \rm\dfrac{0 +b }{2}\bigg) \\ \\ \rm \longrightarrow1= \dfrac{a +0}{2}\\ \\ \rm \longrightarrow1 \times 2 = {a +0}\\ \\ \rm \longrightarrow2 = {a +0}\\ \\ \rm \longrightarrow2 = {a } \\ \\ \\ \\ \rm \longrightarrow1= \dfrac{0 + b}{2}\\ \\ \rm \longrightarrow1 \times 2= 0 + b\\ \\ \rm \longrightarrow 2= 0 + b\\ \\ \rm \longrightarrow 2= b$

a = 2 and b = 2

Now, we have to show that (1/a)+(1/b) = 1

RHS = 1

LHS = (1/a)+(1/b)

$\rm \implies\dfrac{1}{a} + \dfrac{1}{b} \\ \\ \rm put \: a = 2 \: and \: b = 2 \\ \\ \rm \implies\dfrac{1}{2} + \dfrac{1}{2}\\ \\ \rm \implies\dfrac{1 + 1}{2}\\ \\ \rm \implies\dfrac{2}{2}\\ \\ \rm \implies1$

Therefore , RHS = LHS

hence proved

Answer 2

Answer:

a way gwueqheh gwgeji r eqg qf u atul of Sri way ku faraxsan tahay inay ku caawiso ma tihid qofka qaata ee ma aha inaad heshid qaate ma tihid qaataha loogu talagalay mana tihid qaataha loogu talagalay mana tihid adreeskii loogu tala galay