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Find the distance between the points (3,1)(3,1) and (0,5)(0,5).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units

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Q. Find the distance between the points (3,1)(3,1) and (0,5)(0,5).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula.\newlineThe coordinates are given as (3,1)(3,1) for the first point and (0,5)(0,5) for the second point. The distance formula is ((x2−x1)2+(y2−y1)2)\sqrt{((x_2-x_1)^2 + (y_2-y_1)^2)}.
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineDistance: (0−3)2+(5−1)2\sqrt{(0-3)^2 + (5-1)^2}
  3. Calculate X-coordinate Difference: Calculate the difference between the x-coordinates and square it. \(0−3-3)^22 = (−3-3)^22 = 99\
  4. Calculate Y-coordinate Difference: Calculate the difference between the y-coordinates and square it.\newline(5−1)2=(4)2=16(5-1)^2 = (4)^2 = 16
  5. Find Square Root: Add the squares of the differences and find the square root. 9+16=25=5\sqrt{9 + 16} = \sqrt{25} = 5

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