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Find the distance between the points (1,0)(1,0) and (9,6)(9,6).\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 (1,0)(1,0) and (9,6)(9,6).\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 coordinates are given as (x1,y1)=(1,0)(x_1, y_1) = (1, 0) and (x2,y2)=(9,6)(x_2, y_2) = (9, 6). The 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:\newlineDistance = (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  2. Substitute into Formula: Substitute the coordinates into the distance formula.\newlineDistance = (9−1)2+(6−0)2\sqrt{(9 - 1)^2 + (6 - 0)^2}
  3. Calculate Differences: Calculate the differences (9−1)(9 - 1) and (6−0)(6 - 0).(9−1)=8(9 - 1) = 8(6−0)=6(6 - 0) = 6
  4. Square the Differences: Square the differences.\newline(8)2=64(8)^2 = 64\newline(6)2=36(6)^2 = 36
  5. Add Squares: Add the squares of the differences.\newline64+36=10064 + 36 = 100
  6. Take Square Root: Take the square root of the sum to find the distance.\newlineDistance = 100\sqrt{100}\newlineDistance = 1010

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