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Find the distance between the points (5,4)(5,4) and (2,8)(2,8).\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 (5,4)(5,4) and (2,8)(2,8).\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 distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a plane is given by the formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.\newlineHere, we have (x1,y1)=(5,4)(x_1, y_1) = (5, 4) and (x2,y2)=(2,8)(x_2, y_2) = (2, 8).
  2. Substitute into Distance Formula: Substitute the coordinates into the distance formula.\newlineDistance = (2−5)2+(8−4)2\sqrt{(2-5)^2 + (8-4)^2}
  3. Calculate Squares of Differences: Calculate the squares of the differences.\newlineCalculate (2−5)2(2-5)^2 and (8−4)2(8-4)^2.\newline(2−5)2=(−3)2=9(2-5)^2 = (-3)^2 = 9\newline(8−4)2=42=16(8-4)^2 = 4^2 = 16
  4. Add Squares of Differences: Add the squares of the differences.\newlineAdd 99 and 1616 to get 2525.\newline9+16=259 + 16 = 25
  5. Take Square Root for Distance: Take the square root of the sum to find the distance.\newlineDistance = 25\sqrt{25}\newlineDistance = 55

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