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Find the distance between the points (4,5)(4,5) and (1,9)(1,9).\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 (4,5)(4,5) and (1,9)(1,9).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\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 (4,5)(4,5) and (1,9)(1,9), we have (x1,y1)=(4,5)(x_1, y_1) = (4, 5) and (x2,y2)=(1,9)(x_2, y_2) = (1, 9).
  2. Apply Distance Formula: Using the distance formula, we substitute the coordinates of the points into the formula: (1−4)2+(9−5)2\sqrt{(1-4)^2 + (9-5)^2}.
  3. Calculate Differences: Calculate the differences: (1−4)=−3(1-4) = -3 and (9−5)=4(9-5) = 4.
  4. Square Differences: Square the differences: (−3)2=9(-3)^2 = 9 and (4)2=16(4)^2 = 16.
  5. Add Squares: Add the squares: 9+16=259 + 16 = 25.
  6. Find Square Root: Take the square root of the sum: 25=5\sqrt{25} = 5.

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