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Find the distance between the points (10,1)(10,1) and (2,7)(2,7).\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 (10,1)(10,1) and (2,7)(2,7).\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round.\newline______ units
  1. Distance Formula Explanation: To find the distance between two points in a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. For the points (10,1)(10,1) and (2,7)(2,7), we have (x1,y1)=(10,1)(x_1, y_1) = (10, 1) and (x2,y2)=(2,7)(x_2, y_2) = (2, 7).
  2. Calculate X-Coordinate Difference: First, we calculate the difference in the x-coordinates: (x2−x1)=(2−10)=−8(x_2 - x_1) = (2 - 10) = -8. Squaring this difference gives us (−8)2=64(-8)^2 = 64.
  3. Calculate Y-Coordinate Difference: Next, we calculate the difference in the y-coordinates: (y2−y1)=(7−1)=6(y_2 - y_1) = (7 - 1) = 6. Squaring this difference gives us (6)2=36(6)^2 = 36.
  4. Add Squares of Differences: Now, we add the squares of the differences in the xx and yy coordinates: 64+36=10064 + 36 = 100.
  5. Find the Distance: Finally, we take the square root of the sum to find the distance: 100=10\sqrt{100} = 10. This is the distance between the two points.

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