Find the coordinates of the point that divides the line segment joining P(1, 2) and Q(7, 8) internally in the ratio 1 : 2.

Step 1: Identify given values

We are given two points, P and Q, and the ratio in which a point divides the line segment PQ internally. Let the coordinates of P be $(x_1, y_1)$ and Q be $(x_2, y_2)$. The given ratio is $m_1 : m_2$.

Step 2: Recall the Section Formula

To find the coordinates of a point R(x, y) that divides the line segment joining two points $(x_1, y_1)$ and $(x_2, y_2)$ internally in the ratio $m_1 : m_2$, we use the section formula.

Step 3: Substitute the values into the formula

Now, we substitute the identified values of $x_1, y_1, x_2, y_2, m_1,$ and $m_2$ into the section formula to find the $x$ and $y$ coordinates of the point R.

Step 4: Calculate the coordinates

Perform the arithmetic operations to simplify the expressions for $x$ and $y$. This will give us the final coordinates of the point R.

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).
• 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
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