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Find the distance between the points (9,7)(9,7) and (1,1)(1,1).\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 (9,7)(9,7) and (1,1)(1,1).\newline\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline\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)=(9,7)(x_1, y_1) = (9, 7) and (x2,y2)=(1,1)(x_2, y_2) = (1, 1). The distance formula is (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 = (1−9)2+(1−7)2\sqrt{(1-9)^2 + (1-7)^2}
  3. Calculate Differences: Calculate the differences (1−9)(1-9) and (1−7)(1-7).(1−9)=−8(1-9) = -8 and (1−7)=−6(1-7) = -6
  4. Square the Differences: Square the differences.\newline(−8)2=64(-8)^2 = 64 and (−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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