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Find the distance between the points (8,10)(8,10) and (0,4)(0,4).\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 (8,10)(8,10) and (0,4)(0,4).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Identify 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 (8,10)(8,10) and (0,4)(0,4), we have (x1,y1)=(8,10)(x_1, y_1) = (8, 10) and (x2,y2)=(0,4)(x_2, y_2) = (0, 4).
  2. Calculate X-coordinate Difference: Calculate the difference in the x-coordinates: (x2−x1)=(0−8)=−8(x_2 - x_1) = (0 - 8) = -8. Then square this difference: (−8)2=64(-8)^2 = 64.
  3. Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates: (y2−y1)=(4−10)=−6(y_2 - y_1) = (4 - 10) = -6. Then square this difference: (−6)2=36(-6)^2 = 36.
  4. Add Squares of Differences: Add the squares of the differences in the x and y coordinates: 64+36=10064 + 36 = 100.
  5. Find Distance: Take the square root of the sum to find the distance: 100=10\sqrt{100} = 10.

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