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Find the distance between the points (6,8)(6,8) and (3,4)(3,4).\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 (6,8)(6,8) and (3,4)(3,4).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units
  1. Identify Coordinates and Formula: Identify the coordinates of the two points and the formula to use.\newlineWe have the points (6,8)(6,8) and (3,4)(3,4). To find the distance between two points in a plane, we use the distance formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. Plug Coordinates into Formula: Plug the coordinates into the distance formula. Using the points (6,8)(6,8) as (x1,y1)(x_1, y_1) and (3,4)(3,4) as (x2,y2)(x_2, y_2), we get the distance as (3−6)2+(4−8)2\sqrt{(3-6)^2 + (4-8)^2}.
  3. Calculate Differences and Square: Calculate the differences and square them.\newlineCalculate (3−6)2(3-6)^2 and (4−8)2(4-8)^2.\newline(3−6)2=(−3)2=9(3-6)^2 = (-3)^2 = 9\newline(4−8)2=(−4)2=16(4-8)^2 = (-4)^2 = 16
  4. Add Squares and Find Square Root: Add the squares and find the square root.\newlineNow we add the squares of the differences: 9+16\sqrt{9 + 16}.\newline9+16=25=5\sqrt{9 + 16} = \sqrt{25} = 5

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