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Find the distance between the points (1,4)(1,4) and (9,10)(9,10).\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 (1,4)(1,4) and (9,10)(9,10).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline______ units
  1. Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula.\newlineThe coordinates are given as (x1,y1)=(1,4)(x_1, y_1) = (1, 4) and (x2,y2)=(9,10)(x_2, y_2) = (9, 10). The distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineDistance = (9−1)2+(10−4)2\sqrt{(9 - 1)^2 + (10 - 4)^2}
  3. Calculate Differences: Calculate the differences (9−1)(9 - 1) and (10−4)(10 - 4).(9−1)=8(9 - 1) = 8 and (10−4)=6(10 - 4) = 6
  4. Square the Differences: Square the differences.\newline(8)2=64(8)^2 = 64 and (6)2=36(6)^2 = 36
  5. Add Squares: Add the squares of the differences.\newline64+36=10064 + 36 = 100
  6. Take Square Root: Take the square root of the sum to find the distance. 100=10\sqrt{100} = 10

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