The formula for the midpoint $M$ of a line segment joining two points $C(x_1, y_1)$ and $D(x_2, y_2)$ is:

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

We are given:

• $M(-5, 7)$
• $D(-6, 5)$
• $C(x, y)$ (to be found)

Step 1: Solve for $x$-coordinate

Using the midpoint formula:

$\frac{x + (-6)}{2} = -5$

Multiply both sides by 2:

$x - 6 = -10$

Add 6 to both sides:

$x = -4$

Step 2: Solve for $y$-coordinate

Using the midpoint formula:

$\frac{y + 5}{2} = 7$

Multiply both sides by 2:

$y + 5 = 14$

Subtract 5 from both sides:

$y = 9$

Final Answer:

The coordinates of point $C$ are $(-4, 9)$.

Would you like a step-by-step verification or additional details?

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Related Questions:

1. How do you find the midpoint if given two points?
2. What is the distance between points C and D?
3. How do you find the equation of the line passing through C and D?
4. What are the properties of midpoints in geometry?
5. How can this method be applied in three-dimensional space?

Tip:

Always check your calculations by substituting the found coordinates back into the midpoint formula!