CAT Exam > CAT Questions > Directions for Questions use the following i...
Start Learning for Free
Directions for Questions use the following information and answer the following questions:
ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.
Then D is
- a)3 km east and 1 km north of A
- b)3 km east and √3 km north of A
- c)√3 km east and 1 km south of A
- d)√3 km west and 3 km north of A
- e)Inadequate data
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Directions for Questions use the following information and answer the...
Given Information:
- ABC forms an equilateral triangle.
- B is 2 km from A.
- A person starts walking from B in a direction parallel to AC.
- The person stops when he reaches a point D directly east of C.
- The person then reverses direction and walks till he reaches a point E directly south of C.
To find:
The coordinates of point D.
Solution:
Step 1: Determine the coordinates of points A, B, and C.
Since ABC is an equilateral triangle, all sides are equal in length. Let's assume the length of each side is 's'.
From the given information, we know that B is 2 km from A. Therefore, AB = 2 km.
As ABC is an equilateral triangle, all angles are 60 degrees.
Using the Law of Cosines, we can find the length of BC:
BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(60)
s^2 = (2)^2 + AC^2 - 2 * 2 * AC * 0.5
s^2 = 4 + AC^2 - 2AC
s^2 - AC^2 + 2AC - 4 = 0
AC^2 - 2AC = s^2 - 4
AC^2 - 2AC + 1 = s^2 - 4 + 1
(AC - 1)^2 = s^2 - 3
Now, since ABC is an equilateral triangle, the coordinates of point A can be taken as (0, 0).
Using Pythagoras' theorem, we can find the coordinates of point C:
AC^2 = (AC - 1)^2 + s^2
AC^2 = (AC - 1)^2 + (s^2 - 3)
AC^2 = AC^2 - 2AC + 1 + s^2 - 3
2AC = s^2 - 2
AC = (s^2 - 2)/2
Therefore, the coordinates of point C are (((s^2 - 2)/2), 0).
Since B is 2 km from A, the coordinates of point B are (2, 0).
Step 2: Determine the coordinates of point D.
The person starts walking from point B in a direction parallel to AC. This means the y-coordinate remains 0, and only the x-coordinate changes.
Since the person stops at point D, which is directly east of C, the x-coordinate of D will be the same as the x-coordinate of C.
Therefore, the coordinates of point D are (((s^2 - 2)/2), 0).
Step 3: Determine the answer choice that matches the coordinates of point D.
According to the answer choices:
a) 3 km east and 1 km north of A
b) 3 km east and √3 km north of A
c) √3 km east and 1 km south of A
d) √3 km west and 3 km north of A
e) Inadequate data
From our calculations, the x-coordinate of point D is (((s^2 - 2)/2
- ABC forms an equilateral triangle.
- B is 2 km from A.
- A person starts walking from B in a direction parallel to AC.
- The person stops when he reaches a point D directly east of C.
- The person then reverses direction and walks till he reaches a point E directly south of C.
To find:
The coordinates of point D.
Solution:
Step 1: Determine the coordinates of points A, B, and C.
Since ABC is an equilateral triangle, all sides are equal in length. Let's assume the length of each side is 's'.
From the given information, we know that B is 2 km from A. Therefore, AB = 2 km.
As ABC is an equilateral triangle, all angles are 60 degrees.
Using the Law of Cosines, we can find the length of BC:
BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(60)
s^2 = (2)^2 + AC^2 - 2 * 2 * AC * 0.5
s^2 = 4 + AC^2 - 2AC
s^2 - AC^2 + 2AC - 4 = 0
AC^2 - 2AC = s^2 - 4
AC^2 - 2AC + 1 = s^2 - 4 + 1
(AC - 1)^2 = s^2 - 3
Now, since ABC is an equilateral triangle, the coordinates of point A can be taken as (0, 0).
Using Pythagoras' theorem, we can find the coordinates of point C:
AC^2 = (AC - 1)^2 + s^2
AC^2 = (AC - 1)^2 + (s^2 - 3)
AC^2 = AC^2 - 2AC + 1 + s^2 - 3
2AC = s^2 - 2
AC = (s^2 - 2)/2
Therefore, the coordinates of point C are (((s^2 - 2)/2), 0).
Since B is 2 km from A, the coordinates of point B are (2, 0).
Step 2: Determine the coordinates of point D.
The person starts walking from point B in a direction parallel to AC. This means the y-coordinate remains 0, and only the x-coordinate changes.
Since the person stops at point D, which is directly east of C, the x-coordinate of D will be the same as the x-coordinate of C.
Therefore, the coordinates of point D are (((s^2 - 2)/2), 0).
Step 3: Determine the answer choice that matches the coordinates of point D.
According to the answer choices:
a) 3 km east and 1 km north of A
b) 3 km east and √3 km north of A
c) √3 km east and 1 km south of A
d) √3 km west and 3 km north of A
e) Inadequate data
From our calculations, the x-coordinate of point D is (((s^2 - 2)/2
Free Test
FREE
| Start Free Test |
Community Answer
Directions for Questions use the following information and answer the...
Based on the data given, we can draw the following figure
In triangle BDN,
BD2 = BN2 + DN2
4 = 1 + DN2
Hence, DN = √3
Hence, option 2 is correct
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer?
Question Description
Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer?.
Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions for Questions use the following information and answer the following questions:ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa)3 km east and 1 km north of Ab)3 km east and √3 km north of Ac)√3 km east and 1 km south of Ad)√3 km west and 3 km north of Ae)Inadequate dataCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup