Question

if B(x,y) is a point on the line segment joining the point A(a,b) and C(b,a), then prove that x+y=a+b

Answer 1

Answer:

If B divides AC into K ratio 1then

Answer 2

Answer with Step-by-step explanation:

Let B(x,y) divides the line joining points A(a,b) and C(b,a) in the ratio k:1

Section formula :$x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

We have $m_1=k,m_2=1$

$x_1=a,y_1=b,x_2=b,y_2=a$

Using the formula

$x=\frac{bk+a}{k+1},y=\frac{ak+b}{k+1}$

$x+y=\frac{bk+a}{k+1}+\frac{ak+b}{k+1}$

$x+y=\frac{bk+ak+a+b}{k+1}$

$x+y=\frac{k(a+b)+a+b}{k+1}$

$x+y=\frac{(a+b)(k+1)}{k+1}=a+b$

LHS=RHS

Hence, proved.

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