# Endpoint Calculator

Initial Position Coordinates

Center Point Coordinates

## Related Converters

Endpoint calculator helps you find the missing endpoint of a line segment if you know its starting point and midpoint coordinate values. The calculator also gives you a graphical representation along with step-by-step calculations.

## What Is An Endpoint?

“ An endpoint is the point at which a line segment ends”

There are two endpoints on a line segment located at opposite ends of the segment.

## Endpoint Formula:

The formula to calculate the endpoint of a line segment depends on what you already know about any of the following:

Scenario 1: Knowing Starting Point and Other Endpoint:

Let's consider the starting point as coordinates (X1, Y1) and the other endpoint as (X2, Y2).
If you want to find the missing endpoint, let it have coordinates (X3, Y3)!

Use the midpoint formula:

• Midpoint X = (X1 + X2) / 2
• Midpoint Y = (Y1 + Y2) / 2

Once you have the midpoint coordinates, you can use them to solve for the missing endpoint (X3, Y3) using the following formulas:

• X_3 = 2 x Midpoint X - X2
• Y_3 = 2 x Midpoint Y - Y2

Scenario 2: Knowing Midpoint and Other Endpoint:

Let’s consider the given endpoint as coordinates (X1, Y1) and the midpoint as (X2, Y2). If you want to find the missing endpoint, let it be coordinates (X3, Y3).

Use the following formulas to solve directly for the missing endpoint:

• X_3 = 2 x Midpoint X - X1
• Y_3 = 2 x Midpoint Y - Y1

Remember to replace X1, Y1, X2, Y2, X3, and Y3 with the actual coordinates of your points. These formulas will give you the coordinates of the missing endpoint of the line segment.

## How to Find an Endpoint?

Let’s say, you are building a treehouse and need a rope ladder to climb up. You know the ladder starts at the ground (point A) and reaches the treehouse platform (point B). You also know the ladder's midpoint is halfway up (point M). But how long is the ladder?

To find the endpoint of the ladder, you need to take note of the clues you find:

Point A (ground):

• x_1 = 0: This indicates the horizontal position (x-axis) of point A. Since it's on the ground, it has a horizontal displacement of 0 units.
• y_1 = 0: This indicates the vertical position (y-axis) of point A. Being on the ground, its vertical displacement is also 0 units.

Point M (midpoint):

• x_2 = 3: This represents the horizontal position (x-axis) of the ladder's midpoint. We have measured this distance on the ladder.
• y_2 = 6: This represents the vertical position (y-axis) of the midpoint. We know it's halfway up the ladder, which we measured as 6 units from the ground.

Given Data:

• Point A (ground): x_1 = 0, y_1 = 0
• Point M (midpoint): x_2 = 3, y_2 = 6
• Point B (treehouse): We want to find x_3 and y_3

Put the values into the endpoint formula:

• Missing endpoint x: x_3 = 2 * x2 - x1 = 2 * 3 - 0 = 6
• Missing endpoint y: y_3 = 2 * y2 - y1 = 2 * 6 - 0 = 12

Therefore,

• Point B (treehouse): x_3 = 6, y_3 = 12

So, the rope ladder is 6 units long on the x-axis and 12 units long on the y-axis, making it a total of 13.45 units long!

### Common Examples of Endpoint:

Scenario Starting Point Midpoint Ending Point
Walking a Path Entrance Park Bench Exit
Reading a Book Chapter 1 Page 100 Chapter 10