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Find the distance between the points (4,10)(4,10) and (0,7)(0,7).\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 (4,10)(4,10) and (0,7)(0,7).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\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)=(4,10)(x_1, y_1) = (4, 10) and (x2,y2)=(0,7)(x_2, y_2) = (0, 7). The distance formula is (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineDistance = (0−4)2+(7−10)2\sqrt{(0-4)^2 + (7-10)^2}
  3. Calculate and Square Differences: Calculate the differences and square them.\newline(0−4)2=(−4)2=16(0-4)^2 = (-4)^2 = 16\newline(7−10)2=(−3)2=9(7-10)^2 = (-3)^2 = 9
  4. Add Squares of Differences: Add the squares of the differences. 16+9=2516 + 9 = 25
  5. Find Distance: Take the square root of the sum to find the distance. \newlineDistance = 25=5\sqrt{25} = 5

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