The coordinate of the point that divides the line segment joining the points (3,4) and (-5,-7) internally in the ratio 3: 2 is ____.

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Detailed Solution

The coordinate of the point that divides the line segment joining the points (3,4) and (-5,-7) internally in the ratio 3: 2 is

− 95, − 135

.
We have been given,
The line segment joining the points (3,4) and (-5,-7) is divided in the ratio 3: 2.
Using the section formula,

(\frac{{mx}_{2} + {nx}_{1}}{m + n}, \frac{{my}_{2} + {ny}_{1}}{m + n})

Assuming the coordinates of the point of division are,

a, b

Calculating the value of (a, b).
Substituting

m = 3, n = 2, x_{2} = - 5, x_{1} = 3, y_{2} = - 7, and y_{1} = 4

, in the section formula,

\Rightarrow (\frac{3 \times (- 5) + 2 \times 3}{3 + 2}, \frac{3 \times (- 7) + 2 \times 4)}{3 + 2})

\Rightarrow (- \frac{9}{5}, - \frac{13}{5})

Therefore, the coordinates of the point are

− 95, − 135

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