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Find the distance between the points (4,10) and (2,1). Write your answer as a whole number or a fully simplified radical expression. Do not round. ◻ units

Find the distance between the points (4,10) (4,10) and (2,1) (2,1) .\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round. □ \square \newlineunits

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Full solution

Q. Find the distance between the points (4,10) (4,10) and (2,1) (2,1) .\newlineWrite your answer as a whole number or a fully simplified radical expression. Do not round. □ \square \newlineunits
  1. Given Points: We have:
    Points: (4,10)(4, 10) and (2,1)(2, 1)
    Find the values of x1x_1, x2x_2, y1y_1 and y2y_2 from the given points.
    x1=4x_1 = 4
    y1=10y_1 = 10
    x2=2x_2 = 2
    y2=1y_2 = 1
  2. Distance Formula: We know: Distance formula: d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} x1=4 x_1 = 4 , y1=10 y_1 = 10 , x2=2 x_2 = 2 and y2=1 y_2 = 1 Substitute the values of x1 x_1 , y1 y_1 , x2 x_2 , y2 y_2 in the distance formula. d=(x2−x1)2+(y2−y1)2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d=(2−4)2+(1−10)2 d = \sqrt{(2 - 4)^2 + (1 - 10)^2}
  3. Simplify Calculation: Simplify (2−4)2+(1−10)2(2-4)^2 + (1-10)^2.
    (2−4)2+(1−10)2(2-4)^2 + (1-10)^2
    = (−2)2+(−9)2(-2)^2 + (-9)^2
    = 44 + 8181
    = 8585
  4. Find Distance: We have: d=85d = \sqrt{85} Find the distance between the points (4,10)(4, 10) and (2,1)(2, 1). d=85d = \sqrt{85} Distance between the points (4,10)(4, 10) and (2,1)(2, 1) is 85\sqrt{85} units.

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