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Madison competes in a robotics challenge. For one task, she programs her robot to move to locations on a grid. The robot picks up a ball at point A(-6,3) and moves it first to point B(-6,-4) and then to point C(-2,-4) along straight paths. Each unit on the grid represents 1ft. What is the total distance Madison's robot moves with the ball?

Madison competes in a robotics challenge. For one task, she programs her robot to move to locations on a grid. The robot picks up a ball at point A(−6,3) A(-6,3) and moves it first to point B(−6,−4) B(-6,-4) and then to point C(−2,−4) C(-2,-4) along straight paths. Each unit on the grid represents 1ft 1 \mathrm{ft} . What is the total distance Madison's robot moves with the ball?

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Q. Madison competes in a robotics challenge. For one task, she programs her robot to move to locations on a grid. The robot picks up a ball at point A(−6,3) A(-6,3) and moves it first to point B(−6,−4) B(-6,-4) and then to point C(−2,−4) C(-2,-4) along straight paths. Each unit on the grid represents 1ft 1 \mathrm{ft} . What is the total distance Madison's robot moves with the ball?
  1. Calculate Distance A to B: Calculate the distance from point A to point B.\newlineSince points A and B have the same x-coordinate (−6-6), the robot moves vertically from A to B. The distance between two points with the same x-coordinate is the absolute difference between their y-coordinates.\newlineDistance from A to B = ∣|y-coordinate of A - y-coordinate of B∣| = ∣3−(−4)∣|3 - (-4)| = ∣3+4∣|3 + 4| = 77 ft
  2. Calculate Distance B to C: Calculate the distance from point B to point C.\newlineSince points B and C have the same y-coordinate (−4-4), the robot moves horizontally from B to C. The distance between two points with the same y-coordinate is the absolute difference between their x-coordinates.\newlineDistance from B to C = ∣|x-coordinate of B −- x-coordinate of C∣| = ∣−6−(−2)∣|-6 - (-2)| = ∣−6+2∣|-6 + 2| = 44 ft
  3. Find Total Distance: Add the distances from Step 11 and Step 22 to find the total distance the robot moves.\newlineTotal distance = Distance from A to B + Distance from B to C = 7 ft+4 ft=11 ft7 \, \text{ft} + 4 \, \text{ft} = 11 \, \text{ft}

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