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Find the distance between the points (4,9)(4,9) and (0,6)(0,6).\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 (4,9)(4,9) and (0,6)(0,6).\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 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}.\newlineHere, we have (x1,y1)=(4,9)(x_1, y_1) = (4, 9) and (x2,y2)=(0,6)(x_2, y_2) = (0, 6).
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineDistance = (0−4)2+(6−9)2\sqrt{(0-4)^2 + (6-9)^2}
  3. Calculate Squares of Differences: Calculate the squares of the differences.\newlineCalculate (0−4)2(0-4)^2 and (6−9)2(6-9)^2.\newline(0−4)2=(−4)2=16(0-4)^2 = (-4)^2 = 16\newline(6−9)2=(−3)2=9(6-9)^2 = (-3)^2 = 9
  4. Add Squares of Differences: Add the squares of the differences.\newlineAdd 1616 and 99 to get 2525.\newline16+9=2516 + 9 = 25
  5. Take Square Root: Take the square root of the sum to find the distance.\newlineThe square root of 2525 is 55.\newline25=5\sqrt{25} = 5

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