Find the coordinates of the missing endpoint if B is the midpoint of line AC; C(-5,4), B(-2,5)

To find the coordinates of the missing endpoint \( A(x_1, y_1) \) when point \( B(x_2, y_2) \) is the midpoint of line \( AC \) and \( C(x_3, y_3) \) is given, you can use the midpoint formula:

\[
B\left(x_2, y_2\right) = \left(\frac{x_1 + x_3}{2}, \frac{y_1 + y_3}{2}\right)
\]

Given:
- \( C(-5, 4) \) so \( x_3 = -5 \) and \( y_3 = 4 \)
- \( B(-2, 5) \) so \( x_2 = -2 \) and \( y_2 = 5 \)

Now, let's solve for \( x_1 \) and \( y_1 \):

1. For the \( x \)-coordinate:
   \[
   -2 = \frac{x_1 + (-5)}{2}
   \]
   Multiply both sides by 2:
   \[
   -4 = x_1 - 5
   \]
   Add 5 to both sides:
   \[
   x_1 = 1
   \]

2. For the \( y \)-coordinate:
   \[
   5 = \frac{y_1 + 4}{2}
   \]
   Multiply both sides by 2:
   \[
   10 = y_1 + 4
   \]
   Subtract 4 from both sides:
   \[
   y_1 = 6
   \]

So, the coordinates of the missing endpoint \( A \) are \( \boxed{(1, 6)} \).

Would you like any further details or have any other questions?

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Here are 5 related questions:

1. How do you find the midpoint of a line segment when both endpoints are given?
2. What is the distance between points \( A(1, 6) \) and \( C(-5, 4) \)?
3. How would the calculation change if you were given the coordinates of \( A \) and \( B \) instead?
4. What happens to the coordinates if point \( B \) moves further along the line segment \( AC \)?
5. How can you verify that \( B(-2, 5) \) is the correct midpoint?

**Tip:** Always double-check your midpoint calculations by ensuring that the midpoint coordinates are exactly halfway between the two endpoints.

Learn how to find the coordinates of endpoint A using the midpoint formula with point B(-2, 5) as the midpoint of line segment AC. Detailed step-by-step solution provided.

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