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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) (5,−3)(5,-3)\newline(C) (9,7)(9,7)\newline(D) (−7,0)(-7,0)

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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) (5,−3)(5,-3)\newline(C) (9,7)(9,7)\newline(D) (−7,0)(-7,0)
  1. Calculate distance formula: Calculate the distance from each point to (1,4)(1,4) using the distance formula: Distance=((x2−x1)2+(y2−y1)2)\text{Distance} = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}, where (x1,y1)=(1,4)(x_1, y_1) = (1, 4) and (x2,y2)(x_2, y_2) are the coordinates of each point.
  2. Compare calculated distances: Compare each calculated distance to 80\sqrt{80} to determine which points are exactly 80\sqrt{80} units away.

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