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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 $5 + 8 + \sqrt{89}$ 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.