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Find the distance between the points (1,3)(1,3) and (9,9)(9,9).\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 (1,3)(1,3) and (9,9)(9,9).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\newline_____\_\_\_\_\_ units
  1. Identify formula: Identify the formula to calculate the distance between two points.\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 distance formula: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.\newlineFor the points (1,3)(1,3) and (9,9)(9,9), we have (x1,y1)=(1,3)(x_1, y_1) = (1, 3) and (x2,y2)=(9,9)(x_2, y_2) = (9, 9).
  2. Substitute coordinates: Substitute the coordinates of the points into the distance formula.\newlineDistance: (9−1)2+(9−3)2\sqrt{(9-1)^2 + (9-3)^2}
  3. Calculate differences: Calculate the differences (9−1)(9-1) and (9−3)(9-3).(9−1)=8(9-1) = 8(9−3)=6(9-3) = 6
  4. Square 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. 100=10\sqrt{100} = 10

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