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Find the distance between the points (0,3)(0,3) and (8,9)(8,9).\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 (0,3)(0,3) and (8,9)(8,9).\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 (0,3)(0,3) and (8,9)(8,9). To find the distance between two points in a plane, we use the distance 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.\newlineUsing the points (0,3)(0,3) as (x1,y1)(x_1, y_1) and (8,9)(8,9) as (x2,y2)(x_2, y_2), we get:\newlineDistance =((8−0)2+(9−3)2)= \sqrt{((8-0)^2 + (9-3)^2)}.
  3. Calculate Differences and Squares: Calculate the differences and square them.\newlineCalculate (8−0)2(8-0)^2:\newline(8−0)2=82=64(8-0)^2 = 8^2 = 64.\newlineCalculate (9−3)2(9-3)^2:\newline(9−3)2=62=36(9-3)^2 = 6^2 = 36.\newlineNow we have:\newlineDistance = 64+36\sqrt{64 + 36}.
  4. Add and Find Square Root: Add the squares and find the square root.\newlineAdd 64+3664 + 36 to get 100100.\newlineNow take the square root:\newlineDistance = 100=10\sqrt{100} = 10.\newlineThe distance between the points (0,3)(0,3) and (8,9)(8,9) is 1010 units.

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