Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.

Step 1: Identify given values

We are given two points, $(x_1, y_1) = (4, -3)$ and $(x_2, y_2) = (8, 5)$. We are also given the ratio in which the line segment joining these points is divided, which is $m_1:m_2 = 3:1$.

Step 2: Recall the 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 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 $P$.

Step 4: Calculate the x-coordinate

First, we calculate the $x$ -coordinate. We perform the multiplication and addition in the numerator, then divide by the sum of the ratios.

Step 5: Calculate the y-coordinate

Next, we calculate the $y$ -coordinate. Similar to the $x$ -coordinate, we perform the operations in the numerator and then divide by the sum of the ratios.

Step 6: State the coordinates of the point

Combining the calculated $x$ and $y$ coordinates, we get the coordinates of the point that divides the line segment in the given ratio.

More from this chapter

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• Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
• 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)
• Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).
• Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis, and find the coordinates of the point of division.
• Find the coordinates of a point P(x, y) lying on the line 2x + y = 6 such that the sum of its distances from the fixed points A(1, 1) and B(4, 5) is minimized

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