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Find the distance between the points (7,5)(7,5) and (3,8)(3,8).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline______ units

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Q. Find the distance between the points (7,5)(7,5) and (3,8)(3,8).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline______ units
  1. Identify Points: To find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the distance formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. For the points (7,5)(7,5) and (3,8)(3,8), we have (x1,y1)=(7,5)(x_1, y_1) = (7, 5) and (x2,y2)=(3,8)(x_2, y_2) = (3, 8).
  2. Substitute into Formula: Substitute the coordinates into the distance formula: (3−7)2+(8−5)2\sqrt{(3-7)^2 + (8-5)^2}.
  3. Calculate Differences: Calculate the differences: (3−7)=−4(3-7) = -4 and (8−5)=3(8-5) = 3.
  4. Square the Differences: Square the differences: (−4)2=16(-4)^2 = 16 and (3)2=9(3)^2 = 9.
  5. Add Squares: Add the squares: 16+9=2516 + 9 = 25.
  6. Take Square Root: Take the square root of the sum: 25=5\sqrt{25} = 5.

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