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Find the distance between the points (8,1)(8,1) and (5,5)(5,5).\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 (8,1)(8,1) and (5,5)(5,5).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units
  1. Identify Coordinates: To find the distance between two points in a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. Let's apply this formula to the points (8,1)(8,1) and (5,5)(5,5).
  2. Substitute Values: First, we identify the coordinates of the two points. We have (x1,y1)=(8,1)(x_1, y_1) = (8, 1) and (x2,y2)=(5,5)(x_2, y_2) = (5, 5). Now we substitute these values into the distance formula.
  3. Calculate X-coordinate Difference: Calculate the difference in the x-coordinates: (x2−x1)=(5−8)=−3(x_2 - x_1) = (5 - 8) = -3. Squaring this difference gives us (−3)2=9(-3)^2 = 9.
  4. Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates: (y2−y1)=(5−1)=4(y_2 - y_1) = (5 - 1) = 4. Squaring this difference gives us (4)2=16(4)^2 = 16.
  5. Add Squares and Find Distance: Now we add the squares of the differences in the xx and yy coordinates: 9+16=259 + 16 = 25.
  6. Add Squares and Find Distance: Now we add the squares of the differences in the xx and yy coordinates: 9+16=259 + 16 = 25.Finally, we take the square root of the sum to find the distance: 25=5\sqrt{25} = 5. This is the distance between the two points.

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