CAT Exam > CAT Questions > If A (3, 5), B (-3, - 4), C (7, 10) are the v...
Start Learning for Free
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex are
- a)(10, 19)
- b)(15, 10)
- c)(19, 10)
- d)(15, 19)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogra...
Midpoint of A (3, 5) and C (7, 10) = M(5, (15/2))
∴ Mild points of BD = M(5, (15/2))
B(-5, -4) and D(x, y)
∴(-5+x)/2 = 5, x = 10 + 5 = 15
(-4 + y)/2 = 15/2, y = 15 + 4 = 19
Co-ordinates of fourth vertex D = (15, 19)
Free Test
FREE
| Start Free Test |
Community Answer
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogra...
To find the fourth vertex of the quadrilateral, we need to determine the coordinates of the missing vertex. Since we are given the coordinates of three vertices, we can use the properties of quadrilaterals to find the missing vertex.
Quadrilaterals have several properties, one of which is that the opposite sides are equal in length. So, if we can find the lengths of the sides AB, BC, and CA, we can determine which side is opposite to the missing vertex and find its length.
Finding the Length of the Sides:
Using the distance formula, we can find the lengths of the sides AB, BC, and CA.
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-3 - 3)^2 + (-4 - 5)^2)
= sqrt((-6)^2 + (-9)^2)
= sqrt(36 + 81)
= sqrt(117)
BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((7 - (-3))^2 + (10 - (-4))^2)
= sqrt((10)^2 + (14)^2)
= sqrt(100 + 196)
= sqrt(296)
CA = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((7 - 3)^2 + (10 - 5)^2)
= sqrt((4)^2 + (5)^2)
= sqrt(16 + 25)
= sqrt(41)
Identifying the Opposite Side:
Now, let's compare the lengths of the sides AB, BC, and CA. We can see that AB and CA have the same length, sqrt(117), which means they are opposite sides. Therefore, the missing vertex should be opposite to the side BC.
Finding the Missing Vertex:
To find the missing vertex, we need to consider the coordinates of the known vertices. Since AB and CA are opposite sides, the x-coordinate of the missing vertex should be the same as the x-coordinate of C, which is 7. Similarly, the y-coordinate of the missing vertex should be the same as the y-coordinate of A, which is 5.
Therefore, the missing vertex should have the coordinates (7, 5).
Comparing with Answer Options:
Now let's compare this result with the given answer options:
a) (10, 19): This is not the correct answer as it does not match the coordinates we found.
b) (15, 10): This is not the correct answer as it does not match the coordinates we found.
c) (19, 10): This is not the correct answer as it does not match the coordinates we found.
d) (15, 19): This is not the correct answer as it does not match the coordinates we found.
None of the given answer options match the coordinates we found, so there seems to be an error. It is possible that the correct answer is not among the given options.
Quadrilaterals have several properties, one of which is that the opposite sides are equal in length. So, if we can find the lengths of the sides AB, BC, and CA, we can determine which side is opposite to the missing vertex and find its length.
Finding the Length of the Sides:
Using the distance formula, we can find the lengths of the sides AB, BC, and CA.
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-3 - 3)^2 + (-4 - 5)^2)
= sqrt((-6)^2 + (-9)^2)
= sqrt(36 + 81)
= sqrt(117)
BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((7 - (-3))^2 + (10 - (-4))^2)
= sqrt((10)^2 + (14)^2)
= sqrt(100 + 196)
= sqrt(296)
CA = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((7 - 3)^2 + (10 - 5)^2)
= sqrt((4)^2 + (5)^2)
= sqrt(16 + 25)
= sqrt(41)
Identifying the Opposite Side:
Now, let's compare the lengths of the sides AB, BC, and CA. We can see that AB and CA have the same length, sqrt(117), which means they are opposite sides. Therefore, the missing vertex should be opposite to the side BC.
Finding the Missing Vertex:
To find the missing vertex, we need to consider the coordinates of the known vertices. Since AB and CA are opposite sides, the x-coordinate of the missing vertex should be the same as the x-coordinate of C, which is 7. Similarly, the y-coordinate of the missing vertex should be the same as the y-coordinate of A, which is 5.
Therefore, the missing vertex should have the coordinates (7, 5).
Comparing with Answer Options:
Now let's compare this result with the given answer options:
a) (10, 19): This is not the correct answer as it does not match the coordinates we found.
b) (15, 10): This is not the correct answer as it does not match the coordinates we found.
c) (19, 10): This is not the correct answer as it does not match the coordinates we found.
d) (15, 19): This is not the correct answer as it does not match the coordinates we found.
None of the given answer options match the coordinates we found, so there seems to be an error. It is possible that the correct answer is not among the given options.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer?
Question Description
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer?.
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer?.
Solutions for If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. 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 If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex area)(10, 19)b)(15, 10)c)(19, 10)d)(15, 19)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup