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Find the distance between the points (6,0)(6,0) and (3,4)(3,4). Write your answer as a whole number or a fully simplified radical expression. Do not round.

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Full solution

Q. Find the distance between the points (6,0)(6,0) and (3,4)(3,4). Write your answer as a whole number or a fully simplified radical expression. Do not round.
  1. Identify Coordinates: Identify the coordinates of the two points.\newlineWe have the points (6,0)(6, 0) and (3,4)(3, 4). Let's denote these points as follows:\newlinePoint A (x1,y1)=(6,0)(x_1, y_1) = (6, 0)\newlinePoint B (x2,y2)=(3,4)(x_2, y_2) = (3, 4)
  2. Apply Distance Formula: Apply the distance formula.\newlineThe distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. We will use this formula to find the distance between points AA and BB.
  3. Substitute Coordinates: Substitute the coordinates into the distance formula.\newlineUsing the coordinates from Step 11, we get:\newlined=(3−6)2+(4−0)2d = \sqrt{(3 - 6)^2 + (4 - 0)^2}
  4. Calculate Differences: Calculate the differences and square them.\newline(3−6)2=(−3)2=9(3 - 6)^2 = (-3)^2 = 9\newline(4−0)2=42=16(4 - 0)^2 = 4^2 = 16
  5. Add Squared Differences: Add the squared differences.\newline9+16=259 + 16 = 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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