A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km…
2018
A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H while D is 3 km east of G and F is 2 km north of G. I is situated just in middle of B and C while E is just in middle of H and D.
What is the approximate distance between A and G ?
- A.
2.4 km
- B.
2 km
- C.
2.24 km
- D.
1 km
Show answer & explanation
Correct answer: C
To find the distance between house A and house G, we can establish a coordinate system with house B at the origin (0, 0).
Step-by-Step Coordinate Mapping
B = (0, 0)
C is 2 km east of B: C = (2, 0)
A is 1 km north of B: A = (0, 1)
H is 2 km south of A: Since A is at (0, 1), H is at (0, 1 - 2) = (0, -1)
G is 1 km west of H: Since H is at (0, -1), G is at (0 - 1, -1) = (-1, -1)
Calculating the Distance
We now have the coordinates for A and G:
A = (0, 1)
G = (-1, -1)
To find the distance, we use the Euclidean distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Distance = √((-1 - 0)² + (-1 - 1)²)
Distance = √((-1)² + (-2)²)
Distance = √(1 + 4)
Distance = √5
√5 is approximately 2.24 km