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The Distance Formula can be used to find the distance between two points. d = (x1, y1) (x2 - x1)2 + (y2 - y1)2 (x2, y2) A line segment is graphed on the coordinate plane. The distance between the points can be found using the Distance Formula. (-4 , 1) (2 , 3) Check each step of the work. Then hit OK. The work is shown below to find the distance between the points shown. (-4 , 1) x1 y1 d = x2 (2 , 3) 62 + 22 (2 - -4)2 + (3 - 1)2 y2 (x2 - x1)2 + (y2 - y1)2 = 40 The exact distance between the points is √40. Round the distance to the nearest tenth.Use a calculator. (-4 , 1) √40 ≈ units (2 , 3) Your Turn! Find the distance between the points. Start by writing the coordinates. ( , ) ( , ) Drag the appropriate notation onto the diagram. ( x1 ? 2 , 1 y1 ) ( x2 5 , y2 ? 4 ) d = Plug the values into the distance formula. ( – )2 + ( – )2 (x2 - x1)2 + (y2 - y1)2 ( x1 2 , 1 y1 ) ( x2 5 , 4 y2 ) d = Simplify under the radical (5 – 2)2 + ( 4 – 1)2 2 + 2 (x2 - x1)2 + (y2 - y1)2 ( x1 2 , 1 y1 ) ( x2 5 , 4 y2 ) d = Continue to simplify. (5 – 2)2 + ( 4 – 1)2 32 + 32 (x2 - x1)2 + (y2 - y1)2 + ( x1 2 , 1 y1 ) ( x2 5 , 4 y2 ) d = Write the exact answer asa radical. (5 – 2)2 + ( 4 – 1)2 9 + 9 32 + 32 (x2 - x1)2 + (y2 - y1)2 = √ ( x1 2 , 1 y1 ) ( x2 5 , 4 y2 ) d = Round to the nearest tenth. (5 – 2)2 + ( 4 – 1)2 9 + 9 32 + 32 (x2 - x1)2 + (y2 - y1)2 = √ 18 ( Round to the nearest tenth: √18 ≈ x1 2 , 1 y1 ) ( x2 5 , 4 y2 ) |