Question

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

Endpoint: (−9, −4), midpoint: (0, 8)

Question 7 options:

(-4.5, -6)


(9, 20)


(-6.5, 4)


(6.5, -9)

Answer 1

To find the other endpoint of the line segment when given one endpoint and the midpoint, you can use the midpoint formula.

The formula for the midpoint \( M \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

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

In this case, you have:

- Endpoint \( A(-9, -4) \)
- Midpoint \( M(0, 8) \)

Let the other endpoint be \( B(x, y) \). Using the midpoint formula, we set up the following equations:

\[
\frac{-9 + x}{2} = 0 \quad \text{(1)}
\]
\[
\frac{-4 + y}{2} = 8 \quad \text{(2)}
\]

Now solve these equations.

From equation (1):

\[
-9 + x = 0 \implies x = 9
\]

From equation (2):

\[
-4 + y = 16 \implies y = 20
\]

So, the other endpoint \( B \) is:

\[
(9, 20)
\]

Thus, the answer is:

**(9, 20)**