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Which of these points are 80\sqrt{80} units away from (1,4)(1,4)? Select all that apply.\newlineMulti-select Choices:\newline(A) (−3,−4)(-3,-4)\newline(B) (9,7)(9,7)\newline(C) (−7,0)(-7,0)\newline(D) (5,−3)(5,-3)

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Full solution

Q. Which of these points are 80\sqrt{80} units away from (1,4)(1,4)? Select all that apply.\newlineMulti-select Choices:\newline(A) (−3,−4)(-3,-4)\newline(B) (9,7)(9,7)\newline(C) (−7,0)(-7,0)\newline(D) (5,−3)(5,-3)
  1. Calculate distance formula: Calculate the distance from (1,4)(1,4) to each point using the distance formula: distance=(x2−x1)2+(y2−y1)2\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
  2. Check point A distance: Check if 80\sqrt{80} matches the required distance for point A.
  3. Calculate distance to point B: Calculate the distance to point B (9,7)(9,7).
  4. Check point B distance: Check if 73\sqrt{73} matches the required distance for point B.
  5. Calculate distance to point C: Calculate the distance to point C (−7,0)(-7,0).
  6. Check point C distance: Check if 80\sqrt{80} matches the required distance for point C.
  7. Calculate distance to point D: Calculate the distance to point D (5,−3)(5,-3).
  8. Check point D distance: Check if 65\sqrt{65} matches the required distance for point D.

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