Math Problem Statement

Find the midpoint between (-1, 2) and (-4, -3).

Solution

The image you uploaded shows the midpoint formula and an example to work on. The midpoint formula is:

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

This formula calculates the average of the x-values and the average of the y-values from two given points.

The problem asks you to find the midpoint between the points (1,2)(-1, 2) and (4,3)(-4, -3). To solve this:

  1. Find the average of the x-values: 1+(4)2=52=2.5\frac{-1 + (-4)}{2} = \frac{-5}{2} = -2.5

  2. Find the average of the y-values: 2+(3)2=12=0.5\frac{2 + (-3)}{2} = \frac{-1}{2} = -0.5

Thus, the midpoint is (2.5,0.5)(-2.5, -0.5).

Would you like more details or a step-by-step breakdown? Feel free to ask!

Here are some additional related questions for you:

  1. How do you interpret the midpoint in a geometric context?
  2. What happens if the two points are in a different quadrant of the coordinate plane?
  3. Can the midpoint formula be used for three-dimensional coordinates?
  4. How can you find the midpoint if only the distance between two points is given?
  5. What is the significance of the midpoint in real-world applications, like navigation or design?

Tip: Always double-check the signs of the values in the formula, as errors in adding or subtracting negative numbers can lead to mistakes!

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Math Problem Analysis

Mathematical Concepts

Midpoint Formula
Coordinate Geometry
Averages

Formulas

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

Theorems

Midpoint Theorem

Suitable Grade Level

Grades 7-9