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Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is
- a)60
- b)13
- c)17
- d)7
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Location of B is north of A and location of C is east of A. The distan...
Here is the arrangement.
Applying the Pythagoras theorem:
BC2 = AB2 + AC2 = 52 + 122 =25 + 144 = 169.
So BC = 13.
So BC = 13.
Most Upvoted Answer
Location of B is north of A and location of C is east of A. The distan...
Given information:
- Location of B is north of A
- Location of C is east of A
- Distance AB = 5 km
- Distance AC = 12 km
To find the shortest distance between B and C, we can use the Pythagorean theorem.
1. Drawing a diagram:
Let's draw a diagram to visualize the positions of A, B, and C. Assume that A is at the origin (0,0) on a coordinate plane.
C
|
|
A--------B
2. Finding the coordinates of A, B, and C:
Since B is north of A, its y-coordinate will be greater than A's y-coordinate. Let's assume B's coordinates as (0, yB).
Since C is east of A, its x-coordinate will be greater than A's x-coordinate. Let's assume C's coordinates as (xC, 0).
3. Using the distance formula:
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Applying the distance formula for AB and AC:
AB = √((0 - 0)^2 + (yB - 0)^2) = √(yB^2)
AC = √((xC - 0)^2 + (0 - 0)^2) = √(xC^2)
4. Applying the given distances:
From the given information, AB = 5 km and AC = 12 km. Substituting these values in the above equations:
√(yB^2) = 5
√(xC^2) = 12
Squaring both sides:
yB^2 = 25
xC^2 = 144
5. Finding the shortest distance between B and C:
The shortest distance between B and C is the hypotenuse of the right-angled triangle formed by AB and AC. Using the Pythagorean theorem:
shortest distance = √(AB^2 + AC^2)
= √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13 km
Therefore, the shortest distance between the locations B and C is 13 km.
Hence, the correct answer is option 'B'.
- Location of B is north of A
- Location of C is east of A
- Distance AB = 5 km
- Distance AC = 12 km
To find the shortest distance between B and C, we can use the Pythagorean theorem.
1. Drawing a diagram:
Let's draw a diagram to visualize the positions of A, B, and C. Assume that A is at the origin (0,0) on a coordinate plane.
C
|
|
A--------B
2. Finding the coordinates of A, B, and C:
Since B is north of A, its y-coordinate will be greater than A's y-coordinate. Let's assume B's coordinates as (0, yB).
Since C is east of A, its x-coordinate will be greater than A's x-coordinate. Let's assume C's coordinates as (xC, 0).
3. Using the distance formula:
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Applying the distance formula for AB and AC:
AB = √((0 - 0)^2 + (yB - 0)^2) = √(yB^2)
AC = √((xC - 0)^2 + (0 - 0)^2) = √(xC^2)
4. Applying the given distances:
From the given information, AB = 5 km and AC = 12 km. Substituting these values in the above equations:
√(yB^2) = 5
√(xC^2) = 12
Squaring both sides:
yB^2 = 25
xC^2 = 144
5. Finding the shortest distance between B and C:
The shortest distance between B and C is the hypotenuse of the right-angled triangle formed by AB and AC. Using the Pythagorean theorem:
shortest distance = √(AB^2 + AC^2)
= √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13 km
Therefore, the shortest distance between the locations B and C is 13 km.
Hence, the correct answer is option 'B'.
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Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer?
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Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer?.
Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer?.
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Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C isa)60b)13c)17d)7Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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