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

Step 1: Identify given values

We are given two points, $P_1(4, -3)$ and $P_2(8, 5)$, which define the line segment. We are also given the ratio $m:n = 3:1$ in which the point divides the segment internally. Here, $m=3$ and $n=1$.

Step 2: Apply 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 the values

Now, we substitute the identified values into the section formula. For the $x$ -coordinate, we use $m=3$, $x_2=8$, $n=1$, and $x_1=4$. For the $y$ -coordinate, we use $m=3$, $y_2=5$, $n=1$, and $y_1=-3$.

Step 4: Calculate the coordinates

Perform the arithmetic operations to find the values of $x$ and $y$. First, calculate the numerators and denominators, then divide to get the final coordinates.

Step 5: State the final coordinates

The coordinates of the point that divides the line segment joining $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally are $(7, 3)$.

More from this chapter

• Q7. If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b. [2 Marks]
• Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).
• Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
• 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)
• 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.

All Coordinate Geometry solutions →