Question

Which is the other endpoint of a line segment with one endpoint at (-2,-5) and midpoint at (3,2)
A. (1,-3)
B.(2,-6)
C.(5,7)
D.(8,9)
E.(10,14)

Answer 1

To find the other endpoint of a line segment when given one endpoint and the midpoint, we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

In this case:
- One endpoint \( A \) is at \( (-2, -5) \)
- The midpoint \( M \) is at \( (3, 2) \)
- Let the other endpoint be \( B(x_2, y_2) \)

Using the midpoint formula, we set up the equations based on the given values:

1. For the x-coordinates:
\[
\frac{-2 + x_2}{2} = 3
\]

2. For the y-coordinates:
\[
\frac{-5 + y_2}{2} = 2
\]

Now, we solve each equation:

**For the x-coordinate:**
\[
-2 + x_2 = 6 \quad (\text{multiplying both sides by 2})
\]
\[
x_2 = 6 + 2 = 8
\]

**For the y-coordinate:**
\[
-5 + y_2 = 4 \quad (\text{multiplying both sides by 2})
\]
\[
y_2 = 4 + 5 = 9
\]

Thus, the coordinates of the other endpoint \( B \) are \( (8, 9) \).

So the correct answer is **D. (8,9)**.