Math Problem Statement

BC has endpoints at B(2, 6) and C(0, 13). Find the midpoint M of BC.

Write the coordinates as decimals or integers.

Solution

To find the midpoint MM of a line segment BC with endpoints B(x1,y1)B(x_1, y_1) and C(x2,y2)C(x_2, y_2), we use the midpoint formula:

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

Given the coordinates of B(2,6)B(2, 6) and C(0,13)C(0, 13), we substitute into the formula:

M=(2+02,6+132)M = \left( \frac{2 + 0}{2}, \frac{6 + 13}{2} \right) M=(22,192)M = \left( \frac{2}{2}, \frac{19}{2} \right) M=(1,9.5)M = (1, 9.5)

So, the midpoint MM of BC is (1,9.5)(1, 9.5).

Would you like a detailed explanation of how to apply the midpoint formula in other contexts?

Here are 5 related questions:

  1. How do you find the distance between two points?
  2. What is the slope of the line passing through points B and C?
  3. How do you find the equation of a line passing through two points?
  4. What is the equation of a perpendicular bisector of the line segment BC?
  5. How would the midpoint formula change in three-dimensional space?

Tip: The midpoint of a line segment is always halfway between the two endpoints, making it useful for geometry and coordinate problems!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

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

Theorems

Midpoint Theorem

Suitable Grade Level

Grades 6-8