Coordinates of Points Calculator

P₁(0, 0)P₂(0, 0)P(0.00, 0.00)Ratio = 1:1 (50.0%)Given PointsRatio PointConnection Line

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=x1+mm+n(x2x1)

y=y1+mm+n(y2y1)

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
P1(1,2) P2(7,8) P(3.4,4.4)

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.