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Find the distance between the points (4,0)(4,0) and (0,3)(0,3).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units

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Q. Find the distance between the points (4,0)(4,0) and (0,3)(0,3).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units
  1. Define Points: We will use the distance formula to find the distance between the points (4,0)(4,0) and (0,3)(0,3). The distance formula is ((x2−x1)2+(y2−y1)2)\sqrt{((x_2-x_1)^2 + (y_2-y_1)^2)}. Let's denote (4,0)(4,0) as (x1,y1)(x_1 , y_1) and (0,3)(0,3) as (x2,y2)(x_2 , y_2).
  2. Substitute Coordinates: Now we substitute the coordinates into the distance formula: (0−4)2+(3−0)2\sqrt{(0-4)^2 + (3-0)^2}.
  3. Calculate (0−4)2(0-4)^2: Calculate (0−4)2(0-4)^2: (0−4)2=(−4)2=16(0-4)^2 = (-4)^2 = 16.
  4. Calculate (3−0)2(3-0)^2: Calculate (3−0)2(3-0)^2: (3−0)2=32=9(3-0)^2 = 3^2 = 9.
  5. Add Squares: Add the squares of the differences: 16+9\sqrt{16 + 9}.
  6. Calculate Square Root: Calculate the square root of the sum: 25=5\sqrt{25} = 5.

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