While exploring a mountain trail, Emek and Tara received a distress signal from a climber stranded at (8, 7) on their coordinate map. Each coordinate unit represented 1 kilometer. Rescue Station A was at (2, -1), while Station B was at (15, 7). Emek calculated the straight-line distance from Station A to the climber. The horizontal change was 6 kilometers and the vertical change was 8 kilometers, giving a distance of 10 kilometers. From Station B, the climber was 7 kilometers away along the same horizontal line. Tara concluded that Station B offered the shorter approach. To organize the rescue, they also located the midpoint between Station B and the climber at (11.5, 7), where supplies could be placed for the returning team. They compared this with the midpoint of the longer route from Station A, (5, 3), and confirmed their calculations. Using the shorter 7-kilometer route and the planned rest point, the rescue team reached the climber quickly and returned safely.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Compare the coordinates of the two points and notice which coordinate stays the same.
Why is the distance from Station B at (15, 7) to the climber at (8, 7) especially easy to calculate?
They have the same x-coordinate, so only the vertical distance matters.They have the same y-coordinate, so the distance is the difference between their x-coordinates.Both coordinates must be added because the points lie on the same line.Their midpoint has a whole-number x-coordinate.
Correct. Since both points have y-coordinate 7, the route is horizontal and its length is the difference between 15 and 8.
Not quite. Check which coordinate is the same for Station B and the climber.
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Hint
Compare the two route lengths by finding their difference.
Station A is 10 kilometers from the climber, while Station B is 7 kilometers away. How many kilometers shorter is the route from Station B?
Correct. The route from Station B is 3 kilometers shorter.
Check the difference between the 10-kilometer route and the 7-kilometer route.
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Hint
Compare the horizontal distance from 11.5 to each endpoint.
The midpoint between Station B at (15, 7) and the climber at (8, 7) is (11.5, 7). Which statement correctly explains how this midpoint confirms that the supply point divides the route equally?
The supply point is 3.5 kilometers from each endpoint because 15 - 11.5 = 3.5 and 11.5 - 8 = 3.5.The supply point is 7 kilometers from each endpoint because the full route is 7 kilometers.The supply point is 11.5 kilometers from both endpoints because its x-coordinate is 11.5.The supply point divides the route equally only because all three points have y-coordinate 7.
Correct. The midpoint is 3.5 kilometers from Station B and 3.5 kilometers from the climber.
Not quite. A midpoint must be the same distance from both endpoints along the segment.
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Uçurumdaki Kurtarma Rotası
TR
ARC_G09_GM_02_STORY_02
Uçurumdaki Kurtarma Rotası
The Cliffside Rescue Route
EN
ARC_G09_GM_02_STORY_02
The Cliffside Rescue Route