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Find the distance between the points (0,10)(0,10) and (4,7)(4,7).\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 (0,10)(0,10) and (4,7)(4,7).\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 formula to use.\newlineWe have the points (0,10)(0,10) and (4,7)(4,7). The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a plane is given by the formula (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. Substitute into Distance Formula: Substitute the coordinates into the distance formula.\newlineDistance = (4−0)2+(7−10)2\sqrt{(4-0)^2 + (7-10)^2}
  3. Calculate and Square Differences: Calculate the differences and square them.\newline(4−0)2=42=16(4-0)^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 by Taking Square Root: Take the square root of the sum to find the distance.\newlineDistance = 25=5\sqrt{25} = 5

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