Question

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 B is _____.

• A. 13 km
• B. 26 km
• C. $\sqrt{13}$ km
• D. $2\sqrt{13}$ km

Answer 1

The correct option is D $2\sqrt{13}$ km

The coordinates of A, B and C are (-2, -3), (2, 3) and (3, 2).

By Distance formula, $AB=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
On substituiting the values,
$AB=\sqrt{(2+2{)}^2+(3+3{)}^2}\Rightarrow AB=\sqrt{4^2+6^2}\Rightarrow AB=\sqrt{16+36}\Rightarrow AB=2\sqrt{13}km$