The co-ordinate of the point dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 1:2 is……….. .

Answer

To find the coordinates of the point that divides the line segment joining the points A(1, 3) and B(4, 6) in the ratio 1:2, we can use the section formula. The section formula states that if a point P divides the line segment joining two points A(x1, y1) and B(x2, y2) in the ratio m1:m2, then the coordinates of point P (x, y) can be calculated using the following formulas:

\[ x = \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2} \]
\[ y = \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \]

### Step 1: Identify the coordinates and the ratio
- Let A(1, 3) be (x1, y1) and B(4, 6) be (x2, y2).
- The ratio m1:m2 = 1:2, where m1 = 1 and m2 = 2.

### Step 2: Substitute the values into the formulas
Using the section formula:
- For x-coordinate:
\[ x = \frac{1 \cdot 4 + 2 \cdot 1}{1 + 2} \]
\[ x = \frac{4 + 2}{3} = \frac{6}{3} = 2 \]

- For y-coordinate:
\[ y = \frac{1 \cdot 6 + 2 \cdot 3}{1 + 2} \]
\[ y = \frac{6 + 6}{3} = \frac{12}{3} = 4 \]

### Step 3: Combine the coordinates
The coordinates of the point that divides the line segment in the ratio 1:2 are (2, 4).

### Final Answer
The coordinate of the point dividing the line segment joining A(1, 3) and B(4, 6) in the ratio 1:2 is **(2, 4)**.

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