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Distance Between Two Points Worksheet With Answers Pdf

Distance is a fundamental concept of mathematics that helps us measure the length between two points. In geometry, the distance formula is used to measure the distance between two points in a Cartesian coordinate system. The formula is derived from the Pythagorean theorem and is widely used in various fields, including physics, engineering, and computer science.

This article aims to provide a comprehensive guide on the distance between two points worksheet with answers PDF. This worksheet is an excellent tool for students to practice their understanding of the distance formula and develop problem-solving skills. It provides a series of exercises that cover different difficulty levels and requires students to apply the formula to calculate the distance between two points.

What is the Distance Formula?

Distance Formula Image

The distance formula is a mathematical expression that helps us calculate the distance between any two points in a two-dimensional space. The formula is as follows:

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

Where:

  • d: represents the distance between the two points.
  • x1, y1: represents the coordinates of the first point.
  • x2, y2: represents the coordinates of the second point.

How to Use the Distance Formula?

Using the distance formula is relatively easy once you understand the concept. Here is a step-by-step guide on how to use the formula:

  1. Identify the coordinates of the two points in the Cartesian plane.
  2. Substitute the coordinates of the points into the formula.
  3. Simplify the expression by performing the necessary operations.
  4. Take the square root of the result to get the final answer.

Distance Between Two Points Worksheet with Answers PDF

Worksheet With Answers Image

The distance between two points worksheet with answers PDF is a valuable tool for students to master the distance formula. It provides a series of exercises with different difficulty levels that require students to apply the formula to find the distance between two points. The worksheet comes with answers, which allows students to check their work and identify any mistakes they have made.

Here are some examples of exercises that you may find in the worksheet:

Example 1

Find the distance between points A(3, 4) and B(6, 8).

Solution:

  1. Identify the coordinates of the two points.

    2. A(3, 4), B(6, 8)

  2. Substitute the coordinates of the points into the formula.

    3. d = sqrt((6-3)^2 + (8-4)^2)

  3. Simplify the expression by performing the necessary operations.

    4. d = sqrt(9 + 16)

    d = sqrt(25) = 5

  4. Take the square root of the result to get the final answer.

    5. The distance between points A and B is 5 units.

Example 2

Find the distance between points C(-2, 5) and D(3, -2).

Solution:

  1. Identify the coordinates of the two points.

    2. C(-2, 5), D(3, -2)

  2. Substitute the coordinates of the points into the formula.

    3. d = sqrt((3-(-2))^2 + (-2-5)^2)

  3. Simplify the expression by performing the necessary operations.

    4. d = sqrt(25 + 49)

    d = sqrt(74)

  4. Take the square root of the result to get the final answer.

    5. The distance between points C and D is approximately 8.6 units.

Example 3

The coordinates of three vertices of a quadrilateral are A(5, 6), B(9, 8), and C(2, 7). Find the perimeter of the quadrilateral.

Solution:

  1. Identify the coordinates of the three vertices of the quadrilateral.

    2. A(5, 6), B(9, 8), and C(2, 7)

  2. Calculate the distance between each pair of adjacent vertices using the distance formula.

    3. AB = sqrt((9-5)^2 + (8-6)^2) = sqrt(20)

    BC = sqrt((9-2)^2 + (8-7)^2) = sqrt(65)

    CA = sqrt((5-2)^2 + (6-7)^2) = sqrt(10)

  3. Add the distances to find the perimeter.

    4. Perimeter = AB + BC + CA = sqrt(20) + sqrt(65) + sqrt(10) = approximately 18.73 units.

Conclusion

The distance between two points worksheet with answers PDF is an excellent tool for students to practice their understanding of the distance formula. It provides a variety of exercises with different difficulty levels and allows students to check their work using the provided answers. The distance formula is widely used in different fields, and mastering it can enhance problem-solving skills and lead to new discoveries in science, technology, and engineering.

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