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There are two routes to travel from the place A to B by bus. The first bus reaches the place B via C and the second bus reaches the place B from A directly. The position of A, B and C are represented in the following graph.

Based on the above information, answer the following questions.

The distance between A and C is _____.

A

5 km

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B

2 km

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C

\sqrt{5}

km

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D

5 \sqrt{2}

km

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Solution

The correct option is D $5 \sqrt{2}$ km
The coordinates of A, B and C are (-2, -3), (2, 3) and (3, 2).

By Distance formula, $A C = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
On substituiting the values,
$A C = \sqrt{(3 + 2)^{2} + (2 + 3)^{2}} \Rightarrow A C = \sqrt{5^{2} + 5^{2}} \Rightarrow A C = \sqrt{25 + 25} \Rightarrow A C = 5 \sqrt{2} k m$

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