In what ratio the point $(a, b)$ divides the line segment joining the points $(a + b, b + a)$ and $(a - b, b - a)$

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Solution

R.E.F image
Let the line segment joining the points (a+b,b+a) and (a-b,b-a) by the point (a,b) in K:1
using sectional formula.
$x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}$
$a = \frac{k a - k b + a + b}{k + 1}$
$a k + a = a k - b k + a + b$
$b = k b$
$k = 1$

$y = \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}}$
$b = \frac{k b - k a + b + a}{k + 1}$
$b k + b = b k - k a + b + a$
$k a = a$
$k = 1$
Ratio is 1:1

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