In what ratio is the line segment joining the points (3, -5) and (-1, 6) divided by the line y = x ?

CBSE Class 10 Maths PYQ · Coordinate Geometry · Section Formula · 2 Marks · March 2024 · Standard

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642 Marks · March 2024 · Standard

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 $8:7$