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Find the distance between the points (6,4)(6,4) and (10,1)(10,1).\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 (6,4)(6,4) and (10,1)(10,1).\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 (6,4)(6,4) and (10,1)(10,1), we have (x1,y1)=(6,4)(x_1, y_1) = (6, 4) and (x2,y2)=(10,1)(x_2, y_2) = (10, 1).
  2. Substitute into Formula: Substitute the coordinates into the distance formula: (10−6)2+(1−4)2\sqrt{(10-6)^2 + (1-4)^2}.
  3. Calculate Differences: Calculate the differences: (10−6)=4(10-6) = 4 and (1−4)=−3(1-4) = -3.
  4. Square the Differences: Square the differences: 42=164^2 = 16 and (−3)2=9(-3)^2 = 9.
  5. Add Squares: Add the squares: 16+9=2516 + 9 = 25.
  6. Take Square Root: Take the square root of the sum: 25=5\sqrt{25} = 5.

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