Find the coordinates of the point dividing the line segment joining A(3, 5) and B(9, 11) internally in the ratio 2 : 1.

Step 1: Identify Given Information

First, we identify the given coordinates of the two points, A and B, and the ratio in which the line segment AB is divided. Let the coordinates of point A be $(x_1, y_1)$ and point B be $(x_2, y_2)$. The given ratio is $m_1 : m_2 = 2 : 1$.

Step 2: Recall Section Formula

To find the coordinates of a point that divides a line segment internally in a given ratio, we use the section formula. This formula helps us calculate the $x$ and $y$ coordinates of the dividing point.

Step 3: Substitute Values into Formula

Now, we substitute the values of $x_1, y_1, x_2, y_2, m_1,$ and $m_2$ into the section formula. This will give us the expressions for the $x$ and $y$ coordinates of the dividing point.

Step 4: Calculate Coordinates

Finally, we perform the arithmetic operations to calculate the exact values of $x$ and $y$. This gives us the coordinates of the point that divides the line segment.

More from this chapter

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• Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
• Find the relation between x and y if the point (x, y) is equidistant from (7, 1) and (3, 5).
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