Math Problem Statement

To the nearest tenth of a unit, what is the distance between points A and B?

Solution

To calculate the distance between points AA and BB on the coordinate plane, we can use the distance formula, which is:

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

Here, point AA is at coordinates (3,5)(-3, 5), and point BB is at coordinates (6,2)(6, 2).

Substituting the coordinates into the formula:

d=(6(3))2+(25)2d = \sqrt{(6 - (-3))^2 + (2 - 5)^2} d=(6+3)2+(25)2d = \sqrt{(6 + 3)^2 + (2 - 5)^2} d=92+(3)2d = \sqrt{9^2 + (-3)^2} d=81+9d = \sqrt{81 + 9} d=909.49d = \sqrt{90} \approx 9.49

Rounding to the nearest tenth, the distance between points AA and BB is approximately 9.5 units. However, based on the provided multiple-choice options, it seems there is a rounding mismatch, and the nearest choice would be 10.0 units.

Would you like further clarification or more details? Here are some related questions:

  1. How is the distance formula derived?
  2. What is the significance of each term in the distance formula?
  3. Can you explain how to plot points in a coordinate plane?
  4. How would this calculation change in 3D space?
  5. How can we apply the Pythagorean theorem to find the distance between two points?

Tip: Always double-check the units in word problems to ensure consistency in answers.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10