Understanding the One Third Way Point Formula in Coordinate Geometry: Step-by-Step Explanation and Example

The point one third of the way from (x1,y1) to (x2, y2) can be found with the formula (x1+x2/3, y1+y2/3)

To understand how this formula works, let’s break it down step by step

To understand how this formula works, let’s break it down step by step.

Given two points (x1, y1) and (x2, y2), the formula finds the point that is one third of the way between these two points.

To calculate the x-coordinate of this point, we add the x-coordinates of the two points and divide the sum by 3:

x-coordinate = (x1 + x2) / 3

To calculate the y-coordinate of this point, we add the y-coordinates of the two points and divide the sum by 3:

y-coordinate = (y1 + y2) / 3

So, the final formula to find the point one third of the way from (x1, y1) to (x2, y2) is:

(x, y) = ((x1 + x2) / 3, (y1 + y2) / 3)

Let’s work through an example to see how this formula can be applied:

Suppose we have two points: (4, 2) and (10, 6).

First, we calculate the x-coordinate using the formula:

x-coordinate = (4 + 10) / 3 = 14 / 3 = 4.67

Next, we calculate the y-coordinate using the formula:

y-coordinate = (2 + 6) / 3 = 8 / 3 = 2.67

Therefore, the point one third of the way from (4, 2) to (10, 6) is approximately (4.67, 2.67).

You can verify this by plotting the original points on a coordinate plane and measuring the distance between them. Then, you can measure the distance between one of the original points and the point we calculated using the formula. It should be equal to one third of the original distance.

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