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Find the distance between the points (5,6)(5,6) and (1,3)(1,3).\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 (5,6)(5,6) and (1,3)(1,3).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline__\_\_ units
  1. Identify Coordinates: Identify the coordinates of the two points.\newlineWe have the points (5,6)(5, 6) and (1,3)(1, 3). Let's denote these points as follows:\newlinePoint A (x1,y1)=(5,6)(x_1, y_1) = (5, 6)\newlinePoint B (x2,y2)=(1,3)(x_2, y_2) = (1, 3)
  2. Apply Formula: Apply the distance formula.\newlineThe distance dd between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:\newlined=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  3. Substitute Values: Substitute the values into the distance formula.\newlineUsing the coordinates from Step 11, we get:\newlined=(1−5)2+(3−6)2d = \sqrt{(1 - 5)^2 + (3 - 6)^2}
  4. Calculate Differences: Calculate the differences and square them.\newline(1−5)2=(−4)2=16(1 - 5)^2 = (-4)^2 = 16\newline(3−6)2=(−3)2=9(3 - 6)^2 = (-3)^2 = 9
  5. Add Squares: Add the squares of the differences.\newline16+9=2516 + 9 = 25
  6. Take Square Root: Take the square root of the sum to find the distance.\newlined=25=5d = \sqrt{25} = 5

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