Math Problem Statement

Find the midpoint of the segment with the following endpoints. left parenthesis, minus, 4, comma, 8, right parenthesis, and , left parenthesis, 6, comma, 4, right parenthesis (−4,8) and (6,4)

Solution

To find the midpoint of a line segment with endpoints (4,8)(-4, 8) and (6,4)(6, 4), you can use the midpoint formula:

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

Given:

  • x1=4x_1 = -4, y1=8y_1 = 8
  • x2=6x_2 = 6, y2=4y_2 = 4

Substituting these values into the formula:

Midpoint=(4+62,8+42)\text{Midpoint} = \left( \frac{-4 + 6}{2}, \frac{8 + 4}{2} \right)

Simplifying:

Midpoint=(22,122)=(1,6)\text{Midpoint} = \left( \frac{2}{2}, \frac{12}{2} \right) = (1, 6)

So, the midpoint of the segment is (1,6)(1, 6).

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you find the distance between two points on a coordinate plane?
  2. What is the formula to find the slope of a line given two points?
  3. Can you find the equation of the line that passes through the points (4,8)(-4, 8) and (6,4)(6, 4)?
  4. What is the significance of the midpoint in geometry?
  5. How does the concept of midpoint extend to three-dimensional space?

Tip: When finding the midpoint, you're essentially finding the average of the x-coordinates and y-coordinates separately.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry

Formulas

Midpoint formula

Theorems

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Suitable Grade Level

Grades 6-8