In what ratio is the line …
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Sia ? 6 years, 5 months ago
Suppose y-axis divides PQ in the ratio K:1 at R.
Then, the coordinates of the point of division are:
{tex}R \left[ \frac { 3 k + ( - 2 ) \times 1 } { k + 1 } , \frac { 7 k + ( - 3 ) \times 1 } { k + 1 } \right]{/tex}
{tex}= R \left[ \frac { 3 k - 2 } { k + 1 } , \frac { 7 k - 3 } { k + 1 } \right]{/tex}
Since, R lies on y-axis and x-coordinate of every point on y-axis is zero
{tex}\therefore \quad \frac { 3 k - 2 } { k + 1 } = 0{/tex}
{tex}\Rightarrow{/tex} 3k - 2 = 0
{tex}\Rightarrow{/tex} 3k = 2
{tex}\Rightarrow{/tex} {tex}k = \frac { 2 } { 3 }{/tex}
Hence, the required ratio is {tex}\frac { 2 } { 3 } : 1{/tex}
i.e., 2:3
Putting {tex}k = \frac { 2 } { 3 }{/tex}in the coordinates of R
We get, (0, 1)
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