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, 2023

Geometry Difficulty 1.4 Junior Find the answer Canada

In the diagram, points $A$ , $B$ and $C$ are plotted on a $7 \times 10$ grid. Line segments join $A$ , $B$ and $C$ .An ant walks directly from $A$ to $B$ to $C$ to $A$ along these line segments. The distance
that the ant walks is equal to

Pick one

Solution

The path that the ant walks from $A$ to $B$ is vertical and has length 5. The path that the ant walks from $B$ to $C$ is horizontal and has length 8. The path that the ant walks from $C$ to $A$ does not follow the gridlines. To determine the length of $CA$ , we can use the Pythagorean Theorem because $AB$ and $BC$ meet at a right angle. This gives $CA^2 = AB^2 + BC^2 = 5^2 + 8^2 =
25 + 64 = 89 $. Since$ CA > 0 $, then$ CA = $\sqrt{89}$ . Thus, the total distance that the ant walks is

Figure for this problem 5 + 8 + $\sqrt{89}$ $or$ 13 + $\sqrt{89}\$.$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.