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If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:
- a)y − 3x + 9 = 0,3y + x − 3 = 0
- b)y + 3x + 9 = 0,3y + x − 3 = 0
- c)y + 3x + 9 = 0,3y − x + 3 = 0
- d)y − 3x + 3 = 0,3y + x + 9 = 0
Correct answer is option 'A'. Can you explain this answer?
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If one of the diagonals of a square is along the line x = 2y and one ...
As A(3, 0) does not satisfy the diagonal x = 2y.
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∴ A(3,0) does not lie on the diagonal x = 2y.
Let m be the slope of a side passing through A(3, 0).
Equation of the side is: y − 0 = m(x − 3)
⇒ y = m(x − 3)...(i)
Slope of the diagonal x = 2y is 1/2.
Formula to find the angle between two lines:
Where θ is the angle between the two lines and m1 and m2 are the slope of the two lines.
Substituting m = 3, −1/3 in equation (i), we get
Hence, the correct option is (A).
Most Upvoted Answer
If one of the diagonals of a square is along the line x = 2y and one ...
To solve this problem, we need to find the equation of the diagonal that is along the line x = 2y.
Let's assume the coordinates of the other vertex of the square are (a, b). Since the diagonal is along the line x = 2y, we can say that a = 2b.
We are given that one of the vertices is A(3, 0). Using this information, we can find the coordinates of the other vertex.
Since a = 2b, we have 3 = 2b, which gives us b = 3/2. Therefore, the coordinates of the other vertex are (a, b) = (3, 3/2).
Now, let's find the equation of the side of the square through the vertex A(3, 0) and the other vertex (3, 3/2).
The equation of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
(y - y1) = ((y2 - y1)/(x2 - x1)) * (x - x1)
Substituting the values of the points (3, 0) and (3, 3/2) into the formula, we get:
(y - 0) = ((3/2 - 0)/(3 - 3)) * (x - 3)
y = (3/2) * (x - 3)
Simplifying this equation, we get:
y = (3/2)x - (9/2)
Comparing this equation with the given options, we can see that the correct answer is option A: y - 3x + 9 = 0.
Let's assume the coordinates of the other vertex of the square are (a, b). Since the diagonal is along the line x = 2y, we can say that a = 2b.
We are given that one of the vertices is A(3, 0). Using this information, we can find the coordinates of the other vertex.
Since a = 2b, we have 3 = 2b, which gives us b = 3/2. Therefore, the coordinates of the other vertex are (a, b) = (3, 3/2).
Now, let's find the equation of the side of the square through the vertex A(3, 0) and the other vertex (3, 3/2).
The equation of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
(y - y1) = ((y2 - y1)/(x2 - x1)) * (x - x1)
Substituting the values of the points (3, 0) and (3, 3/2) into the formula, we get:
(y - 0) = ((3/2 - 0)/(3 - 3)) * (x - 3)
y = (3/2) * (x - 3)
Simplifying this equation, we get:
y = (3/2)x - (9/2)
Comparing this equation with the given options, we can see that the correct answer is option A: y - 3x + 9 = 0.
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If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. Can you explain this answer?
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If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. 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 If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. Can you explain this answer?.
If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. 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 If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the diagonals of a square is along the line x = 2y and one of its vertices is A(3,0), then its side through this vertex is given by the equations:a)y − 3x + 9 = 0,3y + x − 3 = 0b)y + 3x + 9 = 0,3y + x − 3 = 0c)y + 3x + 9 = 0,3y − x + 3 = 0d)y − 3x + 3 = 0,3y + x + 9 = 0Correct answer is option 'A'. Can you explain this answer?.
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