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: Construct a coordinate diagram according to the given instructions.
Assign the coordinates \((0, 0)\) to Point B.
Consequently, Point A is located 4 km South, at \((0, -4)\).
Point C is situated 3 km East of Point A, resulting in coordinates of \((3, -4)\).
Step 2: Apply the distance formula to calculate the length of BC.
Point B's coordinates are \((0, 0)\), and Point C's coordinates are \((3, -4)\).
\[\text{Distance} = \sqrt{(3 - 0)^2 + (-4 - 0)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km}\]