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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. To determine the displacement of an object, you only have to consider the change in position between the starting point and the ending point. The path followed from one point to the other does not matter.

  3. 25) Name a point that is 2 away from (−1, 5). (0, 6), (0, 4), (−2, 6), or (−2, 4) 26) Name a point that is between 50 and 60 units away from (7, −2) and state the distance between the two points. Many answers. Ex: (60 , −2); 53 units-2-Create your own worksheets like this one with Infinite Geometry. Free trial available at ...

  4. Using the Distance Formula You can use the Distance Formula to fi nd the distance between two points in a coordinate plane. The Distance Formula is related to the Pythagorean Theorem, which you will see again when you work with right triangles in a future course. Distance Formula (AB)2 = (x 2 − x 1)2 + (y 2 − y 1)2 Pythagorean Theorem c2 ...

  5. 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.

  6. Use the Distance Formula Use the Midpoint Formula. Examples: Find the distance between the points (-3,7) and (4,10). Determine whether the triangle formed by points A=(-2,2), B=(2,-1), and C=(5,4) is a right triangle. Find the midpoint of the line segment joining the points P1=(6,-3) and P2=(4,2). Teaching Notes:

  7. Practice Equations of Lines: Slope, Distance, and Midpoint Formulas. Answer these problems, then check your answers using the key on the next page. If you missed something, look at the solutions after the answer key, and if you still don’t understand, watch the review video again.

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