Math Problem Statement

In the standard (x, y) coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (-3, 0) and (7, 4)?

Solution

To solve this problem, we need to find the midpoint of a line segment whose endpoints are (3,0)(-3, 0) and (7,4)(7, 4). The formula for the midpoint of a line segment is:

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

Step-by-Step Solution:

  1. Assign the coordinates:

    • x1=3x_1 = -3, y1=0y_1 = 0
    • x2=7x_2 = 7, y2=4y_2 = 4
  2. Plug these into the midpoint formula: Midpoint=(3+72,0+42)\text{Midpoint} = \left( \frac{-3 + 7}{2}, \frac{0 + 4}{2} \right)

  3. Simplify each coordinate:

    • For the xx-coordinate: 3+72=42=2\frac{-3 + 7}{2} = \frac{4}{2} = 2
    • For the yy-coordinate: 0+42=42=2\frac{0 + 4}{2} = \frac{4}{2} = 2
  4. Thus, the midpoint is: (2,2)(2, 2)

Final Answer:

The correct choice is: A. (2,2)\boxed{\text{A. } (2, 2)}

Would you like me to explain any steps further or explore related concepts?


Related Questions:

  1. What is the distance between the endpoints (3,0)(-3, 0) and (7,4)(7, 4)?
  2. How do you find the slope of a line segment between two points?
  3. What is the equation of the line passing through the points (3,0)(-3, 0) and (7,4)(7, 4)?
  4. If a line segment is extended past one endpoint, what are the coordinates of a new point at twice the original length?
  5. How do you calculate the centroid of a triangle given its vertices?

Tip:

To quickly find midpoints, remember it's simply averaging the xx-coordinates and yy-coordinates separately.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8