Emek and Tara studied a three-dimensional model of two modules that needed a rigid support beam. Using meters as coordinate units, the first connection point was A(1, 2, 1), and the second was B(7, 8, 4). A direct beam between them would have length sqrt((7 - 1)^2 + (8 - 2)^2 + (4 - 1)^2) = 9 meters, which was within the 10-meter limit. However, equipment occupied the central region and blocked the direct path. The engineers had approved two possible clearance points: C(1, 8, 4) and D(7, 2, 4). Tara calculated that the route through C required beams of lengths sqrt(45) and 6 meters, for a total of about 12.71 meters. Emek found that the route through D required sqrt(45) and 6 meters as well. A clearance scan then showed that only the route through D stayed at least 1.5 meters from the equipment. They selected that design, and both beam sections fitted securely, completing the station connection.

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Challenge 1 of 4
Hint
Distance in three dimensions uses the differences in x, y, and z.
A student calculates the direct distance from A(1, 2, 1) to B(7, 8, 4) as sqrt(6^2 + 6^2) and concludes that the beam is about 8.49 meters long. What error did the student make?
The student should have added the coordinate differences instead of squaring them.The student should have used only the difference in the z-coordinates.The student forgot to include the squared z-coordinate difference, 3^2.The student should have multiplied the three coordinate differences.
Correct. The calculation must include all three coordinate differences, including 4 - 1 = 3.
Check the three-dimensional distance formula and make sure all three coordinate directions are included.
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Hint
Find the differences in the x, y, and z coordinates, square them, and add.
For the selected route through D(7, 2, 4), the first beam runs from A(1, 2, 1) to D. What is the square of the length of this beam, in square meters?
Correct. The square of the beam length is 45 square meters.
Use all three coordinate differences from A to D before adding their squares.
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Hint
Length was not the only design requirement. Consider the obstacle and the clearance scan.
The direct route from A to B is 9 meters, while each approved two-section route through C or D is about 12.71 meters. Why did the engineers still select the route through D?
The route through D was shorter than the direct 9-meter route.The direct route was blocked, and only the route through D met the required equipment clearance.The route through C exceeded 10 meters, but the route through D did not.The route through D used only one beam section instead of two.
Correct. The direct path was blocked, and among the approved alternatives, only the route through D provided sufficient clearance.
Compare both the geometric lengths and the clearance conditions described in the story.
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İstasyon Bağlantısını Planlamak
TR
ARC_G11_GM_02_STORY_03
İstasyon Bağlantısını Planlamak
Planning the Station Connector
EN
ARC_G11_GM_02_STORY_03
Planning the Station Connector