Question

Point A is 4 km South of Point B. Point C is 3 km East of Point A. What is the shortest distance between Point B and Point C?

• A. 5 km
• B. 6 km
• C. 7 km
• D. 4 km

Hint:

Use the Pythagoras theorem to find the shortest distance (hypotenuse) when the movement involves perpendicular turns.

Answer 1

The Correct Option is A

Step 1: Draw a coordinate diagram based on directions.
Let Point B be at coordinates \((0, 0)\).
Then Point A is 4 km South ⇒ \((0, -4)\)
Point C is 3 km East of Point A ⇒ \((3, -4)\)
Step 2: Use distance formula to find BC.
Coordinates of B: \((0, 0)\), Coordinates of C: \((3, -4)\)
\[ \text{Distance} = \sqrt{(3 - 0)^2 + (-4 - 0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km} \]