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Find the distance between the points (5,5)(5,5) and (8,1)(8,1).\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 (5,5)(5,5) and (8,1)(8,1).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Distance Formula Explanation: 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}. For the points (5,5)(5,5) and (8,1)(8,1), we have (x1,y1)=(5,5)(x_1, y_1) = (5, 5) and (x2,y2)=(8,1)(x_2, y_2) = (8, 1).
  2. Calculate X-Coordinate Difference: First, we calculate the difference in the x-coordinates: (x2−x1)=(8−5)=3(x_2 - x_1) = (8 - 5) = 3. Then we square this difference: (3)2=9(3)^2 = 9.
  3. Calculate Y-Coordinate Difference: Next, we calculate the difference in the y-coordinates: (y2−y1)=(1−5)=−4(y_2 - y_1) = (1 - 5) = -4. Then we square this difference: (−4)2=16(-4)^2 = 16.
  4. Add Squares of Differences: Now, we add the squares of the differences in the xx and yy coordinates: 9+16=259 + 16 = 25.
  5. Find Square Root: Finally, we take the square root of the sum to find the distance: 25=5\sqrt{25} = 5. This is the distance between the points (5,5)(5,5) and (8,1)(8,1).

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