Math Problem Statement

Given the two end points on the line AB, A (2, 3) and B (-10, 6). Calculate the midpoint of the line

Solution

To find the midpoint MM of the line segment AB, given the two endpoints A(2,3)A(2, 3) and B(10,6)B(-10, 6), 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)

Substituting the coordinates of A(2,3)A(2, 3) and B(10,6)B(-10, 6):

M=(2+(10)2,3+62)M = \left( \frac{2 + (-10)}{2}, \frac{3 + 6}{2} \right)

M=(82,92)M = \left( \frac{-8}{2}, \frac{9}{2} \right)

M=(4,4.5)M = (-4, 4.5)

Thus, the midpoint of the line segment AB is (4,4.5)(-4, 4.5).

Do you want more details or have any questions?

Here are five related questions:

  1. How do you calculate the slope of a line between two points?
  2. What is the distance between the points A(2,3)A(2, 3) and B(10,6)B(-10, 6)?
  3. How do you find the equation of the line passing through points A and B?
  4. What are the coordinates of the midpoint if the endpoints were A(3, 7) and B(-1, -5)?
  5. How does the midpoint change if both points are reflected across the y-axis?

Tip: The midpoint formula averages the x- and y-coordinates to find the center of a line segment.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint Formula

Formulas

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

Theorems

None

Suitable Grade Level

Grades 6-8