Math Problem Statement

Find the distance between points A and B on a graph.

Solution

To find the distance between points AA and BB, we can use the distance formula. The distance formula between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:

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

From the graph:

  • The coordinates of point AA are (6,7)(6, -7).
  • The coordinates of point BB are (7,8)(-7, 8).

Substituting these values into the distance formula:

d=((7)6)2+(8(7))2d = \sqrt{((-7) - 6)^2 + (8 - (-7))^2} d=(13)2+(15)2d = \sqrt{(-13)^2 + (15)^2} d=169+225d = \sqrt{169 + 225} d=394d = \sqrt{394} d19.85 unitsd \approx 19.85 \text{ units}

So, the distance between points AA and BB is approximately 19.85 units.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you derive the distance formula from the Pythagorean theorem?
  2. What is the significance of the signs of the coordinates when applying the distance formula?
  3. Can you apply the distance formula to three-dimensional space?
  4. How can you verify your result visually on a graph?
  5. How would the calculation change if the points were on the same axis?

Tip: Always double-check the coordinates of points when reading from a graph to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9