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Find the distance between the points (0,1)(0,1) and (3,5)(3,5).\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 (0,1)(0,1) and (3,5)(3,5).\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 (0,1)(0,1) for the first point and (3,5)(3,5) 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.\newlineUsing the points (0,1)(0,1) and (3,5)(3,5), we get the following expression for the distance: (3−0)2+(5−1)2\sqrt{(3-0)^2 + (5-1)^2}.
  3. Calculate and Square Differences: Calculate the differences and square them.\newlineCalculate (3−0)2(3-0)^2 which is 323^2 and equals 99.\newlineCalculate (5−1)2(5-1)^2 which is 424^2 and equals 1616.
  4. Add and Find Square Root: Add the squared differences and find the square root.\newlineAdd 9+169 + 16 to get 2525. Then, calculate the square root of 2525, which is 25=5\sqrt{25} = 5.

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