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In what ratio is the line segment joining the points $(3, -5)$ and $(-1, 6)$ divided by the line $y = x$ ?
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Let the required ratio be $K:1$
Coordinates of point P are $(\frac{-K + 3}{K+1}, \frac{6K - 5}{K+1})$
Point P lies on line $y = x \Rightarrow \frac{-K + 3}{K + 1} = \frac{6K - 5}{K+1}$
Solving, we get $K = \frac{8}{7}$
$\therefore$ Required ratio is $8: 7$
Coordinates of point P are $(\frac{-K + 3}{K+1}, \frac{6K - 5}{K+1})$
Point P lies on line $y = x \Rightarrow \frac{-K + 3}{K + 1} = \frac{6K - 5}{K+1}$
Solving, we get $K = \frac{8}{7}$
$\therefore$ Required ratio is $8: 7$