Math Problem Statement

Use the distance formula to find the distance between points A and B. A: (4.3, -1.1) B: (9.2, 4.5)

Solution

To solve the problem of finding the distance between points A and B using the distance formula, we can apply the following formula:

Distance=(x2x1)2+(y2y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Where:

  • A(x1,y1)=(4.3,1.1)A(x_1, y_1) = (4.3, -1.1)
  • B(x2,y2)=(9.2,4.5)B(x_2, y_2) = (9.2, 4.5)

Now let's compute the distance.The distance between points A and B is approximately 7.44 units. Therefore, the correct answer is the first option: 7.44.

Would you like further details or have any questions?

Here are five related questions to deepen understanding:

  1. How does the distance formula relate to the Pythagorean theorem?
  2. Can the distance formula be extended to three-dimensional space?
  3. What are the applications of the distance formula in real-world scenarios?
  4. How do you calculate the midpoint between two points?
  5. How does the slope between two points differ from the distance?

Tip: Remember, when squaring differences in coordinates, negative values always become positive!

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Math Problem Analysis

Mathematical Concepts

Geometry
Distance Between Points
Coordinate Geometry

Formulas

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-10