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There is a well-known formula in mathematics, the distance formula that is closely related to the Pythagorean Theorem, This activity will help you develop that formula

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There is a well-known formula in mathematics, the distance formula that is closely related to the Pythagorean Theorem, This activity will help you develop that formula.

The distance formula is used to find the distance between two points in the coordinate plane, say, (x₁, y₁) and (x₂ y₂). The formula gives the distance between the two points in terms of the coordinates x₁, x₂, y₁ and y₂.

1. a. Find the distance between the points 15, 36and (7, 6).

    b. Describe in detail what you did to find your answer.

2. a. Find the distance between the points (2. Stand (6. 3).

    b. Describe in detail what you did to find your answer.

3. Suppose (x₁, y₁) and (x₂, y₂) are the coordinates of two points.

Generalize what you did in Questions 1 and 2 to create a formula or set of instructions that gives the distance between the two points,

4. Does your generalization work if any of the coordinates x₁, x₂, y₁, and y₂ are negative numbers? Explain with examples.

3. In Question 1, you had two combinations of ticket sales and profit.

• Selling 100 tickets produced a $400 profit.
• Selling 120 tickets produced a $500 profit.

1. What were the two similar combinations in Question 2?
2. In each question two combinations is enough information to allow you to find a rule that describes the situation. What does this have to do with the activity being determined?

4. A line passes through the points (2, 15) and (7, 45). Find an equation for the line, and explain how you got your answer.