Direction TestMTP Sep 24 Series IIQuestion 2329 of 165
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(44-46) Read the information given below to answer these questions A, B, C, D, E, F, G H and I are nine houses C is 2\displaystyle 2 km east of B. A is 1\displaystyle 1 km north of B and H is 2\displaystyle 2 km south of A. G is 1\displaystyle 1 km west of H while D is 3\displaystyle 3 km east of G and F is 2\displaystyle 2 km north of G. I is situated just in the middle of B and C while E just in middle of H and D. Distance between E and I is _______.

Options

A4\displaystyle 4 km
B2\displaystyle 2 km
C1\displaystyle 1 km
D3\displaystyle 3 km
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Correct Answer

✅ Option c — 1\displaystyle 1 km

All Options:

  • A4\displaystyle 4 km
  • B2\displaystyle 2 km
  • C1\displaystyle 1 km
  • D3\displaystyle 3 km

Detailed Solution & Explanation

Let B be at the origin (0,0)\displaystyle (0,0):
- C is 2 km East   ⟹  C=(2,0)\displaystyle \implies C = (2, 0).
- A is 1 km North   ⟹  A=(0,1)\displaystyle \implies A = (0, 1).
- H is 2 km South of A   ⟹  H=(0,−1)\displaystyle \implies H = (0, -1).
- G is 1 km West of H   ⟹  G=(−1,−1)\displaystyle \implies G = (-1, -1).
- D is 3 km East of G   ⟹  D=(2,−1)\displaystyle \implies D = (2, -1).
- F is 2 km North of G   ⟹  F=(−1,1)\displaystyle \implies F = (-1, 1).
- I is the midpoint of B (0,0)\displaystyle (0,0) and C (2,0)\displaystyle (2,0)   ⟹  I=(1,0)\displaystyle \implies I = (1, 0).
- E is the midpoint of H (0,−1)\displaystyle (0,-1) and D (2,−1)\displaystyle (2,-1)   ⟹  E=(1,−1)\displaystyle \implies E = (1, -1).
The distance between E (1,−1)\displaystyle (1, -1) and I (1,0)\displaystyle (1, 0) is exactly 1 km.
Hence, **Option C** is the correct answer.

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