The missing endpoint formula is used when you know one endpoint of a line segment and the midpoint, and you want to find the other endpoint.

Let’s break this down step by step:

Given:

• One endpoint $A(x_1, y_1)$
• The midpoint $M(x_m, y_m)$
• The unknown endpoint $B(x_2, y_2)$

The midpoint formula is:

$M(x_m, y_m) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

To find the missing endpoint $B(x_2, y_2)$, solve for $x_2$ and $y_2$ using the following formulas:

$x_2 = 2x_m - x_1$ $y_2 = 2y_m - y_1$

Example:

If the given endpoint is $A(3, 4)$ and the midpoint is $M(6, 8)$, you can find the other endpoint $B(x_2, y_2)$ as follows:

$x_2 = 2 \times 6 - 3 = 12 - 3 = 9$ $y_2 = 2 \times 8 - 4 = 16 - 4 = 12$

Thus, the missing endpoint $B$ is $(9, 12)$.

Would you like more details or any further explanation on this?

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Here are five related questions to expand your understanding:

1. How do you calculate the midpoint of a line segment?
2. What is the difference between the midpoint formula and the distance formula?
3. How would you find the equation of a line segment given both endpoints?
4. Can the missing endpoint formula be applied in three dimensions?
5. How would you calculate the length of a line segment between two points?

Tip: The midpoint formula is just the average of the corresponding coordinates of the endpoints!