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Find the distance between the points (4,3)(4,3) and (8,6)(8,6).\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 (4,3)(4,3) and (8,6)(8,6).\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 Point A (4,3)(4, 3) and Point B (8,6)(8, 6). We need to find the distance between these two points.\newlineLet's denote the coordinates as follows:\newlinex1=4x_1 = 4, y1=3y_1 = 3 (for Point A)\newlinex2=8x_2 = 8, y2=6y_2 = 6 (for Point B)
  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}\newlineNow we will substitute the values of x1x_1, y1y_1, x2x_2, and y2y_2 into the formula.
  3. Substitute Values: Substitute the values into the distance formula.\newlined=(8−4)2+(6−3)2d = \sqrt{(8 - 4)^2 + (6 - 3)^2}\newlineThis simplifies to:\newlined=(4)2+(3)2d = \sqrt{(4)^2 + (3)^2}
  4. Calculate Squares: Calculate the squares of the differences.\newline(4)2=16(4)^2 = 16\newline(3)2=9(3)^2 = 9\newlineNow we add these two values.\newlined=16+9d = \sqrt{16 + 9}
  5. Add and Find Root: Add the results and find the square root.\newline16+9=2516 + 9 = 25\newlined=25d = \sqrt{25}\newlineThe square root of 2525 is 55.\newlined=5d = 5

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