Math Problem Statement

given A (-1,7) and B (5,3) find the midpoint of AB

Solution

The midpoint of a line segment with endpoints A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2) can be found using the midpoint formula:

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

For the points A(1,7)A(-1, 7) and B(5,3)B(5, 3), the midpoint MM is calculated as follows:

M=(1+52,7+32)M = \left(\frac{-1 + 5}{2}, \frac{7 + 3}{2}\right)

Simplifying this:

M=(42,102)M = \left(\frac{4}{2}, \frac{10}{2}\right)

M=(2,5)M = (2, 5)

So, the midpoint of segment ABAB is (2,5)(2, 5).

Would you like more details or have any questions?

Here are some related questions:

  1. How do you find the distance between two points on a plane?
  2. What is the slope of the line passing through points AA and BB?
  3. How do you find the equation of the line passing through points AA and BB?
  4. Can you find the area of the triangle formed by points AA, BB, and another point CC?
  5. How do you determine if three points are collinear?

Tip: When finding the midpoint, remember that it represents the average of the x-coordinates and y-coordinates of the endpoints.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Midpoint

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8