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Find the distance between the points (2,6)(2,6) and (10,0)(10,0).\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 (2,6)(2,6) and (10,0)(10,0).\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 (2,6)(2,6) for the first point and (10,0)(10,0) 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 (2,6)(2,6) and (10,0)(10,0), we get (10−2)2+(0−6)2\sqrt{(10-2)^2 + (0-6)^2}.
  3. Calculate Coordinate Differences: Calculate the differences for the xx-coordinates and the yy-coordinates.\newlineFor the xx-coordinates: (10−2)=8(10-2) = 8\newlineFor the yy-coordinates: (0−6)=−6(0-6) = -6
  4. Square Coordinate Differences: Square the differences.\newline(8)2=64(8)^2 = 64\newline(−6)2=36(-6)^2 = 36
  5. Add Squares of Differences: Add the squares of the differences. 64+36=10064 + 36 = 100
  6. Find Distance: Take the square root of the sum to find the distance. 100=10\sqrt{100} = 10

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