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  1. Distance Formula and Pythagorean Theorem Example: The distance between (3, 4) and (x, 7) is 5 units. Find x. Using the distance formula: (3 —x)2 + (4—7) x) 3 Solving Graphically (Pythagorean Theorem) Example: b b 3 -5 4 or -4 The length of segment AB is 20. If the coordinate of Ais (5, 1), and the coordinate of B is (-6, y), what is b?

  2. Notes on Distance and Midpoint Formula – (on level) Finding the Distance between 2 points * Plot the points ( -2, 5), (0, 4) and (5, 3). * Find the distance between each set of points. (-2, 5) & (0, -4) = (0, -4) & (5, 3) = (5, 3) & (-2, 5) = The Distance Formula allows you to find the distance between two points. The subscripts (x

  3. (d) Use the Pythagorean theorem to find the distance between A and B (the length of the hypotenuse of the triangle). Use the distance formula to find the distance between the two given points. (You may also use the method from the previous two problems to verify your answer.) 31. (3, 6) and (5, 9) 32. (4, 7) and (2, 3) 33. (-5, 0) and (-2, 6) 34.

  4. Section 2.2: The Distance and Midpoint Formula. For any two points A A A (x1 , y 1) and B (x2 , y 2), the distance between them is given by. (, ) = ( − %) + ( − %) Example 1: Find the distance between the following pair of points. (−3,1) & (1,3) (−2,5) & (1 2,−1) (4,−6) & 23 ,−24. 1) and B.

  5. Use the Distance Formula. We have used the Pythagorean Theorem to find the lengths of the sides of a right triangle. Here we will use this theorem again to find distances on the rectangular coordinate system.

  6. 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.

  7. You can use the Pythagorean theorem to get a general formula for finding the distance between any two points in a coordinate plane. The converse of this theorem is true as well: If the lengths a, b, and c of the sides of a triangle satisfy the equation , then the triangle is a right triangle and c is the length of the hypotenuse. Pythagorean ...