Problem 10 · Compare signed triangular areas · 4 points
Made by AI and not reviewed by a real person.
Erase one dot from Tuesday, Wednesday, or Thursday, then join its two neighbors with a straight line. Which dot makes the area beneath the graph shrink the most? Give its original temperature.
- 12 degrees
- 18 degrees
- 14 degrees
- 10 degrees
- 16 degrees
Show a hint
- The new line makes a triangular change in area. First decide whether each change makes the area grow or shrink.
- All three triangles span two days. Compare each dot’s height with the height of the new line at that day.
Show the answer and solution
Answer: B — 18 degrees
Erasing Tuesday’s 14-degree dot shrinks the area: it is 3 degrees above the line joining 10 and 12. Erasing Thursday’s 18-degree dot shrinks it more: it is 4 degrees above the line joining 12 and 16. The triangles have equal bases, so the taller one removes more area. Wednesday’s 12-degree dot is also 4 degrees from its new line, but it lies below that line, so erasing it makes the area grow instead.