CD has a midpoint at M(–5, –5). Point C is at (–1, –6). Find the coordinates of point D.


To find the coordinates of point \( D \), we can use the midpoint formula. The formula for the midpoint \( M(x_m, y_m) \) of a line segment with endpoints \( C(x_1, y_1) \) and \( D(x_2, y_2) \) is:

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

Given:
- Midpoint \( M = (-5, -5) \)
- Point \( C = (-1, -6) \)

Let \( D(x_2, y_2) \) represent the unknown point.

Using the midpoint formula:

\[
-5 = \frac{-1 + x_2}{2} \quad \text{(for the x-coordinates)}
\]
\[
-5 = \frac{-6 + y_2}{2} \quad \text{(for the y-coordinates)}
\]

Now, solve these equations:

1. For the x-coordinate:
\[
-5 = \frac{-1 + x_2}{2}
\]
Multiply both sides by 2:
\[
-10 = -1 + x_2
\]
Add 1 to both sides:
\[
x_2 = -9
\]

2. For the y-coordinate:
\[
-5 = \frac{-6 + y_2}{2}
\]
Multiply both sides by 2:
\[
-10 = -6 + y_2
\]
Add 6 to both sides:
\[
y_2 = -4
\]

Thus, the coordinates of point \( D \) are \( (-9, -4) \).

Would you like more details or have any questions about the solution?

Here are 5 related questions to expand this topic:
1. How would you find the distance between points \( C \) and \( D \)?
2. What is the slope of the line passing through points \( C \) and \( D \)?
3. Can you calculate the equation of the line passing through \( C \) and \( D \)?
4. How would you solve for the coordinates of point \( D \) if \( C \) were different?
5. What happens to the midpoint if the coordinates of \( C \) and \( D \) are changed?

**Tip:** The midpoint formula is useful when working with geometry problems involving bisectors or symmetry!

CD has a midpoint at M(–5, –5). Point C is at (–1, –6). Find the coordinates of point D.

Learn how to find the coordinates of point D using the midpoint formula, with C at (-1, -6) and midpoint M at (-5, -5). This problem covers essential concepts of coordinate geometry and is suitable for students in Grades 8-10.

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