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Find the distance between the points (7,5)(7,5) and (4,1)(4,1).\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 (7,5)(7,5) and (4,1)(4,1).\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)=(7,5)(x_1, y_1) = (7, 5) and (x2,y2)=(4,1)(x_2, y_2) = (4, 1).
  2. Substitute into Distance Formula: Substitute the coordinates into the distance formula.\newlineDistance = (4−7)2+(1−5)2\sqrt{(4-7)^2 + (1-5)^2}
  3. Calculate and Square Differences: Calculate the differences and square them.\newlineDifference in xx-coordinates: (4−7)=−3(4-7) = -3, and its square is (−3)2=9(-3)^2 = 9.\newlineDifference in yy-coordinates: (1−5)=−4(1-5) = -4, and its square is (−4)2=16(-4)^2 = 16.
  4. Add Squares of Differences: Add the squares of the differences.\newlineSum of the squares: 9+16=259 + 16 = 25.
  5. Find Distance by Taking Square Root: Take the square root of the sum to find the distance.\newlineDistance = 25=5\sqrt{25} = 5 units.

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