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  1. Question 1: Calculate the perimeter of triangle ABC. Question 2: The distance between the points (1, 2) and (16, p) is 17. Find the possible values of p. Question 3: The distance between the points (−3, −4) and (q, 5) is 15. Find the possible values of q.

  2. We seek a formula for the distance between two points: By the Pythagorean Theorem, Since distance is positive, we have: . .

  3. Walk through deriving a general formula for the distance between two points. The distance between the points ( x 1, y 1) and ( x 2, y 2) is given by the following formula: ( x 2 − x 1) 2 + ( y 2 − y 1) 2. In this article, we're going to derive this formula!

  4. The Distance and Midpoint Formulas Learning Objectives: 1. Use the Distance Formula 2. Use the Midpoint Formula Examples: 1. Find the distance between the points (-3,7) and (4,10). 2. Determine whether the triangle formed by points A=(-2,2), B=(2,-1), and C=(5,4) is a right triangle. 3.

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  6. You can use the diagram to generalize the Distance Formula. Consider the two points ( x , y ) , ( x. 2 , y. 1 1 2 ) . ( x , y ) 2 2. Using the Pythagorean Theorem where the distance is the length of the hypotenuse we have: = d ( x − x )

  7. Distance Between Two Points (Pythagorean Theorem) Using the Pythagorean Theorem, find the distance between each pair of points. 1) x y 2) x y 3) x y 4) x y 5) x y 6) x y

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