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Find the distance between the points (0,6)(0,6) and (4,9)(4,9).\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 (0,6)(0,6) and (4,9)(4,9).\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 (0,6)(0,6) and (4,9)(4,9). 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 (0,6)(0,6) as (x1,y1)(x_1, y_1) and (4,9)(4,9) as (x2,y2)(x_2, y_2), we get:\newlineDistance =((4−0)2+(9−6)2)= \sqrt{((4-0)^2 + (9-6)^2)}.
  3. Calculate Differences and Square: Calculate the differences and square them.\newlineCalculate (4−0)2(4-0)^2:\newline(4−0)2=42=16(4-0)^2 = 4^2 = 16.\newlineCalculate (9−6)2(9-6)^2:\newline(9−6)2=32=9(9-6)^2 = 3^2 = 9.
  4. Add and Find Square Root: Add the squares and find the square root.\newlineAdd the results from Step 33:\newline16+9=2516 + 9 = 25.\newlineNow, take the square root of 2525:\newline25=5\sqrt{25} = 5.

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