Nova and Luna received an emergency call from a damaged communication satellite orbiting a distant planet. A coordinate grid showed repair points at A(2, 3), B(8, 7), and C(10, 1). They calculated distances to estimate travel time, determined the midpoint of segment AB to position a relay drone, and compared the slopes of different paths to avoid crossing a field of drifting debris. After selecting the safest repair route and confirming the relay location, they restored the satellite's signal. The communication network came back online, allowing nearby research missions to continue without interruption.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Use the distance formula with horizontal change 8 - 2 and vertical change 7 - 3.
What is the distance between repair points A(2, 3) and B(8, 7) on the coordinate grid?
2√13 units10 units√10 units4√13 unitsCorrect! The distance from A to B is 2√13 units.
Square the horizontal and vertical changes, add them, and then take the square root.
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Hint
Average the two x-coordinates and the two y-coordinates, then add the results.
The relay drone is placed at the midpoint of segment AB, where A is (2, 3) and B is (8, 7). What is the sum of the midpoint's x-coordinate and y-coordinate?
Correct! The midpoint is (5, 5), and 5 + 5 = 10.
Find the midpoint by averaging the matching coordinates before adding them.
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Hint
Calculate each slope and compare their absolute values.
Nova and Luna compare the slopes of paths AB, BC, and AC. Which path has the greatest steepness, meaning the greatest absolute value of slope?
Path ABPath ACPaths AB and AC are equally steepPath BCCorrect! Path BC has slope -3, so its steepness is 3, the greatest of the three.
Steepness depends on the absolute value of slope, so ignore whether the slope is positive or negative.
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