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Find the distance between the points (2,8)(2,8) and (8,0)(8,0).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units

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Full solution

Q. Find the distance between the points (2,8)(2,8) and (8,0)(8,0).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Given Points: To find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the distance formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. For the points (2,8)(2,8) and (8,0)(8,0), we have (x1,y1)=(2,8)(x_1, y_1) = (2, 8) and (x2,y2)=(8,0)(x_2, y_2) = (8, 0).
  2. Calculate x Difference: First, we calculate the difference in the x-coordinates: (x2−x1)=(8−2)=6(x_2 - x_1) = (8 - 2) = 6.
  3. Calculate y Difference: Next, we calculate the difference in the y-coordinates: (y2−y1)=(0−8)=−8(y_2 - y_1) = (0 - 8) = -8. Since we are going to square this value, the negative sign will not affect the result.
  4. Square Differences: Now, we square the differences: (x2−x1)2=62=36(x_2 - x_1)^2 = 6^2 = 36 and (y2−y1)2=(−8)2=64(y_2 - y_1)^2 = (-8)^2 = 64.
  5. Sum of Squares: We add the squared differences to find the sum under the square root: 36+64=10036 + 64 = 100.
  6. Find Distance: Finally, we take the square root of the sum to find the distance: 100=10\sqrt{100} = 10.

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