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Find the distance between the points (9,10)(9, 10) and (3,2)(3, 2). Write your answer as a whole number or a fully simplified radical expression. Do not round.

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Full solution

Q. Find the distance between the points (9,10)(9, 10) and (3,2)(3, 2). Write your answer as a whole number or a fully simplified radical expression. Do not round.
  1. Identify Points: Points: (9,10)(9, 10) and (3,2)(3, 2) Find x1x_1, x2x_2, y1y_1, y2y_2. x1=9x_1 = 9 y1=10y_1 = 10 x2=3x_2 = 3 y2=2y_2 = 2
  2. Apply Distance Formula: Distance formula: d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Substitute values: d=(3−9)2+(2−10)2 d = \sqrt{(3 - 9)^2 + (2 - 10)^2}
  3. Simplify Calculation: Simplify (3−9)2+(2−10)2(3-9)^2 + (2-10)^2.
    (3−9)2+(2−10)2(3-9)^2 + (2-10)^2
    = (−6)2+(−8)2(-6)^2 + (-8)^2
    = 3636 + 6464
    = 100100
  4. Calculate Distance: d=100d = \sqrt{100}\newlined=10d = 10\newlineDistance between the points (9,10)(9, 10) and (3,2)(3, 2) is 1010 units.

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