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  1. 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!

  2. Example 1: distance between two points on a coordinate axes in the first quadrant. Find the distance between the points A and B. Identify the two points and label them \bf{\left(x_1, y_1\right)} and \bf{\left(x_2, y_2\right)} . A=(3,1) and B=(6, 5). Let \left(x_1, y_1\right) =(3, 1) and \left(x_2, y_2\right) =(6, 5).

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

  4. Find the distance between A(-2, 1) and B(1, 3). Distance Formula d = √ """""(x 2 - x 1)2 + ( y 2 - y 1)2 AB = 2√"""""(1 - (-2)) + (3 - (-1))2 AB 2= √""""(3) + (4)2 √= ""25 = 5 Exercises Use the number line to find each measure. 1. BD AB C DE F G 2. DG 3. AF 4. EF 5. BG 6. AG 7. BE + 8. DE Find the distance between each pair of points. 9 ...

  5. . . x. . . 10) . y. . . . x. . . Find the distance between each pair of points uing Pythagorean Theorem. (Sketch a graph and plot the points first). Also, determine the slope between the two points for review. 11) ( , ), ( , ) 12) ( , ), ( , ) 13) ( , ), ( , ) 15) ( , ), ( , )

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  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