About Coordinates of Points Calculator

What is the Coordinates of Points Calculator?

The Coordinates of Points Calculator is a tool that helps determine the coordinates of a point on a line segment, given two points and a ratio. It's particularly useful in geometry, coordinate systems, and various mathematical applications where precise point locations are needed.

Formula

The formula to find the coordinates of a point P(x, y) that divides the line segment between points (x₁, y₁) and (x₂, y₂) in the ratio m:n is:

\[ x = x_1 + \frac{m}{m+n}(x_2 - x_1) \]

\[ y = y_1 + \frac{m}{m+n}(y_2 - y_1) \]

Where:

• (x₁, y₁) are the coordinates of the first point
• (x₂, y₂) are the coordinates of the second point
• m:n is the given ratio

Calculation Steps

1. Identify the coordinates of the two given points: (x₁, y₁) and (x₂, y₂)
2. Determine the ratio m:n
3. Calculate the ratio factor: r = m / (m + n)
4. Apply the formula for x-coordinate: x = x₁ + r(x₂ - x₁)
5. Apply the formula for y-coordinate: y = y₁ + r(y₂ - y₁)
6. Round the results to the desired number of decimal places

Example and Visual Representation

Let's consider an example:

• Point 1: (1, 2)
• Point 2: (7, 8)
• Ratio: 2:3

Calculation:

1. Ratio factor: r = 2 / (2 + 3) = 0.4
2. x = 1 + 0.4(7 - 1) = 3.4
3. y = 2 + 0.4(8 - 2) = 4.4

Therefore, the coordinates of point P are (3.4, 4.4).

This example demonstrates how we can determine the coordinates of a point on a line segment using the given ratio. The visual representation helps to understand the position of the calculated point relative to the two given points.