https://file.aiquickdraw.com/mathbot/file/17265908613799q45sr2i.jpg

To solve this, we can use the midpoint formula. Given the midpoint \( M(x_m, y_m) \) and one endpoint \( A(x_1, y_1) \), we need to find the missing endpoint \( B(x_2, y_2) \).

The midpoint formula is:

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

We are given:
- One endpoint \( A(-1, 4) \)
- Midpoint \( M(-5, -2) \)

Let the missing endpoint be \( B(x_2, y_2) \).

Using the formula for each coordinate:

1. For the \( x \)-coordinate:
\[
-5 = \frac{-1 + x_2}{2}
\]
Multiplying both sides by 2:
\[
-10 = -1 + x_2
\]
Solving for \( x_2 \):
\[
x_2 = -9
\]

2. For the \( y \)-coordinate:
\[
-2 = \frac{4 + y_2}{2}
\]
Multiplying both sides by 2:
\[
-4 = 4 + y_2
\]
Solving for \( y_2 \):
\[
y_2 = -8
\]

Thus, the missing endpoint is \( B(-9, -8) \).

The correct answer is **(-9, -8)**.

Would you like more details or have any questions?

Here are five related questions to consider:
1. How would the formula change if you were given both endpoints and asked to find the midpoint?
2. What happens if the midpoint lies at the origin? How would that affect the coordinates of the endpoints?
3. Can this method be extended to three-dimensional space? How would the midpoint formula look in 3D?
4. How would the solution change if one of the coordinates of the midpoint was a fraction?
5. What happens if the coordinates of both endpoints are the same?

**Tip:** Always double-check both the \( x \)- and \( y \)-coordinate calculations independently to avoid small mistakes!

Find the missing endpoint of a segment with one endpoint at (-1, 4) and the midpoint at (-5, -2).

Solve a geometry problem where you're tasked with finding the missing endpoint of a segment. Given one endpoint at (-1, 4) and the midpoint at (-5, -2), use the midpoint formula to determine the other endpoint.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation