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Find the distance between the points (9,8)(9,8) and (3,0)(3,0).\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 (9,8)(9,8) and (3,0)(3,0).\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 (9,8)(9,8) and (3,0)(3,0), we have (x1,y1)=(9,8)(x_1, y_1) = (9, 8) and (x2,y2)=(3,0)(x_2, y_2) = (3, 0). Let's plug these values into the distance formula.
  2. Calculate X-coordinate Difference: First, calculate the difference in the x-coordinates: (x2−x1)=(3−9)=−6(x_2 - x_1) = (3 - 9) = -6. Squaring this difference gives us (−6)2=36(-6)^2 = 36.
  3. Calculate Y-coordinate Difference: Next, calculate the difference in the y-coordinates: (y2−y1)=(0−8)=−8(y_2 - y_1) = (0 - 8) = -8. Squaring this difference gives us (−8)2=64(-8)^2 = 64.
  4. Add Squares of Differences: Now, add the squares of the differences in the xx and yy coordinates: 36+64=10036 + 64 = 100.
  5. Find the Distance: Finally, 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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