Math Problem Statement

How to calculate the distance between two points A(x1, y1) and B(x2, y2)?

Solution

The image contains the formula for calculating the distance between two points A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2) on a Cartesian plane, labeled as "Jarak AB" which translates to "Distance AB." The formula is based on the Pythagorean theorem:

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

Here’s the breakdown:

  • x1,y1x_1, y_1 are the coordinates of point AA.
  • x2,y2x_2, y_2 are the coordinates of point BB.
  • The formula gives the straight-line distance between the two points, often referred to as the Euclidean distance.

Would you like more details or have any questions?

Here are 5 related questions to further explore the concept:

  1. How do we calculate the distance if one point is the origin (0,0)(0, 0)?
  2. How does this formula apply in 3D space, and what changes are needed?
  3. What is the geometric meaning of the difference between the xx and yy coordinates?
  4. Can this formula be used to determine the perimeter of a triangle with known vertices?
  5. How would you apply this formula if the coordinates were in a different coordinate system (e.g., polar coordinates)?

Tip: This formula is fundamental in geometry and can be extended to higher dimensions by adding more terms for each additional dimension (e.g., 3D, 4D).

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Math Problem Analysis

Mathematical Concepts

Geometry
Distance Formula
Pythagorean Theorem

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-11