Question

Find the other endpoint of the line segment with the given endpoint and midpoint.

Endpoint: (−4, 0), midpoint: (8, 3)

Question 8 options:

(-2, 5.5)


(-1.5, -3.5)


(-6, -1.5)


(20, 6)

Answer 1

To find the other endpoint of a line segment when you have one endpoint and the midpoint, you can use the midpoint formula. The midpoint \( M \) is calculated as follows:

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

Where \( (x_1, y_1) \) is one endpoint and \( (x_2, y_2) \) is the other endpoint. In this case:

- Endpoint \( A = (-4, 0) \)
- Midpoint \( M = (8, 3) \)
- Let the other endpoint be \( B = (x, y) \)

Using the coordinates of the midpoint, we can set up the equations:

\[
8 = \frac{-4 + x}{2}
\]
\[
3 = \frac{0 + y}{2}
\]

Now, let's solve for \( x \) and \( y \).

### Solving for \( x \):

1. Multiply both sides of the first equation by 2:

\[
16 = -4 + x
\]

2. Add 4 to both sides:

\[
x = 16 + 4
\]

\[
x = 20
\]

### Solving for \( y \):

1. Multiply both sides of the second equation by 2:

\[
6 = 0 + y
\]

2. Hence:

\[
y = 6
\]

Thus, the coordinates of the other endpoint \( B \) are \( (20, 6) \).

### Conclusion

The other endpoint of the line segment is \( (20, 6) \).

**Answer: (20, 6)**