We can solve this problem using the formula for the midpoint. The midpoint $M$ of a line segment $AB$, where $A(x_1, y_1)$ and $B(x_2, y_2)$ are the endpoints, is calculated as:

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

Given:

• $M = (6, -3)$
• $A = (5, -5)$

Let $B = (x_2, y_2)$ be the unknown endpoint. We will use the midpoint formula to solve for $x_2$ and $y_2$.

Step 1: Solve for $x_2$

From the formula for the $x$-coordinate of the midpoint: $6 = \frac{5 + x_2}{2}$ Multiply both sides by 2: $12 = 5 + x_2$ Solve for $x_2$: $x_2 = 12 - 5 = 7$

Step 2: Solve for $y_2$

For the $y$-coordinate of the midpoint: $-3 = \frac{-5 + y_2}{2}$ Multiply both sides by 2: $-6 = -5 + y_2$ Solve for $y_2$: $y_2 = -6 + 5 = -1$

Thus, the coordinates of point $B$ are $(7, -1)$.

Would you like further explanation or have any questions?

Related Questions:

1. How do you find the midpoint if both endpoints are known?
2. Can you calculate the distance between two points?
3. How can you use the distance formula in 3D space?
4. What are the coordinates of a point dividing a line segment into a specific ratio?
5. How do transformations affect the midpoint of a line segment?

Tip: Always check your solution by substituting the calculated values back into the original formula to ensure they satisfy the conditions.