Math Problem Statement

Find the distance between C(2, 4) and D(5, 7). Round to the nearest tenth, if necessary.

Solution

To find the distance between two points C(2,4)C(2, 4) and D(5,7)D(5, 7), we can use the distance formula:

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

Where:

  • (x1,y1)=(2,4)(x_1, y_1) = (2, 4) (coordinates of point C)
  • (x2,y2)=(5,7)(x_2, y_2) = (5, 7) (coordinates of point D)

Let me calculate that for you.The distance between the points C(2,4)C(2, 4) and D(5,7)D(5, 7) is approximately 4.2 units, rounded to the nearest tenth.

Would you like more details or have any questions?

Here are 5 related questions you could explore:

  1. How would the distance change if the points were in 3D space?
  2. What is the geometric significance of the distance formula?
  3. Can you calculate the distance between points with negative coordinates?
  4. How can you use the distance formula to find the midpoint of two points?
  5. How does the distance formula relate to the Pythagorean theorem?

Tip: The distance formula is an application of the Pythagorean theorem, where the difference in x and y values represents the legs of a right triangle.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance between two points

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8