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The point $P$ divides the line segment joining the points $A 2, 1$ divides the line segment joining the points and $B (6, 5)$ and in the ratio 1: 3. So, the coordinates of the point P is ____.

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Detailed Solution

The point

P

divides the line segment joining the points

A 2, 1

and

B (6, 5)

in the ratio 1:3. So, the coordinates of the point P is (3,2).
We have been given,
Point

P

divides the line segment joining the points

A 2, 1

and

B (6, 5)

in the ratio 1:3.
Using the section formula,

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

Let the coordinates of P be (a, b).
Using the section rule to determine the values of variables a and b,
Substituting

m = 1, x_{2} = 6, n = 3, x_{1} = 2, y_{2} = 5, and y_{1} = 1

in the section formula,

(a, b) = (\frac{1 \times 6 + 3 \times 2}{1 + 3}, \frac{1 \times 5 + 3 \times 1}{1 + 3})

(a, b) = (\frac{12}{4}, \frac{8}{4})

(a, b) = (3, 2)

Therefore, the coordinates of point P is

(3, 2)

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