Math Problem Statement

Find the coordinates of the midpoint of a segment with the endpoints (2, 8) and (8, 0).

Solution

To find the midpoint of a segment with the given endpoints (2,8)(2, 8) and (8,0)(8, 0), you can use the midpoint formula:

M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

Substitute the given coordinates:

  • x1=2x_1 = 2, y1=8y_1 = 8
  • x2=8x_2 = 8, y2=0y_2 = 0

M=(2+82,8+02)=(102,82)=(5,4)M = \left( \frac{2 + 8}{2}, \frac{8 + 0}{2} \right) = \left( \frac{10}{2}, \frac{8}{2} \right) = (5, 4)

The coordinates of the midpoint are (5,4)(5, 4).

Would you like more details or have any further questions?

Here are five related questions to deepen your understanding:

  1. How do you calculate the distance between two points?
  2. What is the slope of the line segment between (2,8)(2, 8) and (8,0)(8, 0)?
  3. Can you find the equation of the line passing through the points (2,8)(2, 8) and (8,0)(8, 0)?
  4. How do you calculate the midpoint of three-dimensional points?
  5. What happens to the midpoint if both points are translated by a vector?

Tip: The midpoint formula is essentially finding the average of the coordinates, which splits the segment into two equal parts.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint Calculation

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8