Midpoint of a Line Segment with Endpoints X(-6,4) and Y(4,6)

Math Problem Statement

Line segment XY has endpoints at X(-6,4) and Y(4,6). What are the coordinates of the midpoint of the line segment?

The formula for the midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

For the endpoints $X(-6, 4)$ and $Y(4, 6)$ , substitute the values into the formula:

= \left( \frac{-2}{2}, \frac{10}{2} \right) = (-1, 5)$$ Thus, the coordinates of the midpoint are $$(-1, 5)$$. Would you like further clarification or details on how the formula works? Here are 5 related questions for further practice: 1. What is the length of the line segment with endpoints at $$(-6,4)$$ and $$(4,6)$$? 2. How do you calculate the slope of the line passing through $$X(-6, 4)$$ and $$Y(4, 6)$$? 3. If the midpoint is $$(-1, 5)$$, what would be the equation of the line passing through $$X$$ and $$Y$$? 4. Can the midpoint formula be used for three-dimensional points? If so, how? 5. What is the distance from the midpoint $$(-1, 5)$$ to the point $$X(-6, 4)$$? **Tip:** The midpoint formula averages the x-coordinates and y-coordinates of the two endpoints, making it a useful tool in geometry for finding a point that divides a segment into two equal parts.

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Geometry
Coordinate Geometry

Midpoint formula: ( (x1 + x2) / 2, (y1 + y2) / 2 )

Midpoint Theorem

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