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Home » In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.
Class 10 | Exercise 3A | ICSE | Maths | Selina | Shares and Dividend In Two Variables
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.

We should accept the point

    \[P\text{ }\left( x,\text{ }0 \right)\]

on x-hub separates the line portion joining

    \[A\text{ }\left( 4,\text{ }3 \right)\text{ }and\text{ }B\text{ }\left( 2,\text{ }-\text{ }6 \right)\]

in the proportion

    \[k:\text{ }1.\]

Then, at that point, by area recipe, we have

    \[0\text{ }=\text{ }\left( -6k\text{ }+\text{ }3 \right)/\text{ }\left( k\text{ }+\text{ }1 \right)\]

    \[0\text{ }=\text{ }-6k\text{ }+\text{ }3\]

    \[k\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]

Subsequently, the necessary proportion is

    \[1:\text{ }2\]

Also,

    \[x\text{ }=\text{ }\left( 2k\text{ }+\text{ }4 \right)/\text{ }\left( k\text{ }+\text{ }1 \right)\]

    \[=\text{ }\left\{ 2\left( 1/2 \right)\text{ }+\text{ }4 \right\}/\text{ }\left\{ k\text{ }+\text{ }1 \right\}\]

    \[=\text{ }10/3\]

Accordingly, the necessary co-ordinates of the mark of convergence are

    \[\left( 10/3,\text{ }0 \right).\]

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