In what ratio does the point( …

Let the point P(2, y) divide the line segment joining the points A(-2, 2) and B(3, 7) in the ratio {tex} k:1{/tex}
Then, the coordinates of P are
{tex}\left[ \frac { 3 k + ( - 2 ) \times 1 } { k + 1 } , \frac { 7 k + 2 \times 1 } { k + 1 } \right]{/tex}
{tex}= \left[ \frac { 3 k - 2 } { k + 1 } , \frac { 7 k + 2 } { k + 1 } \right]{/tex}
But the coordinates of P are given as {tex} (2, y){/tex}
{tex}\therefore \quad \frac { 3 k - 2 } { k + 1 } = 2{/tex}
{tex}\Rightarrow{/tex} {tex}3k - 2 = 2k + 2{/tex}
{tex}\Rightarrow{/tex} {tex}3k - 2k = 2 + 2{/tex}
{tex}\Rightarrow{/tex} {tex}k = 4{/tex}
{tex}\frac { 7 k + 2 } { k + 1 } = y{/tex}
Putting the values of k, we get
{tex}\frac { 7 \times 4 + 2 } { 4 + 1 } = y{/tex}

{tex}\frac { 30 } { 5 } = y{/tex}
{tex}6 = y{/tex}
i.e., {tex} y = 6{/tex}