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Find the distance between the points (1,2)(1,2) 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 (1,2)(1,2) 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. Apply Distance Formula: 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}. Let's apply this formula to the points (1,2)(1,2) and (5,5)(5,5).
  2. Calculate X-coordinate Difference: First, calculate the difference in the x-coordinates: (5−1)2(5 - 1)^2.(5−1)2=(4)2=16(5 - 1)^2 = (4)^2 = 16.
  3. Calculate Y-coordinate Difference: Next, calculate the difference in the y-coordinates: (5−2)2(5 - 2)^2.(5−2)2=(3)2=9(5 - 2)^2 = (3)^2 = 9.
  4. Add Squares of Differences: Now, add the squares of the differences: 16+916 + 9. \newline16+9=2516 + 9 = 25.
  5. Find Distance: Finally, take the square root of the sum to find the distance: 25\sqrt{25}.\newline25=5\sqrt{25} = 5.

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