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Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C is
Correct answer is '4'. Can you explain this answer?
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Directions: The answer to the following question is a single digit int...
Since the diagonals of a rectangle bisect each other, so the point
lies on y = 2x - C, which gives C = 4
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Directions: The answer to the following question is a single digit int...
= x + 2. What is the sum of the x-coordinates of the other two vertices?
To find the other two vertices of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
The length of the side parallel to the x-axis is the difference between the y-coordinates of the two given points: 3 - 1 = 2.
Since the other two vertices lie on the line y = x + 2, the length of the side parallel to the x-axis is also the difference between the x-coordinates of the two unknown vertices.
Let's call the x-coordinate of one of the unknown vertices x1 and the x-coordinate of the other unknown vertex x2.
From the information above, we have:
x2 - x1 = 2
Since the sum of the x-coordinates of the other two vertices is x1 + x2, we need to find the sum of x1 and x2.
By adding x1 to both sides of the equation x2 - x1 = 2, we get:
x2 = x1 + 2
Substituting this into the sum x1 + x2, we have:
x1 + (x1 + 2) = 2x1 + 2
The sum of the x-coordinates of the other two vertices is 2x1 + 2.
Since we are looking for a single digit integer, we need to find the value of x1 that satisfies the given conditions.
From the given points (1, 3) and (5, 1), we can see that the x-coordinate of the first point is smaller than the x-coordinate of the second point.
Therefore, x1 must be less than x2.
If we try different values of x1, we can find the sum of the x-coordinates of the other two vertices.
Let's start with x1 = 0:
2(0) + 2 = 0 + 2 = 2
The sum of the x-coordinates is 2, but it is not a single digit integer.
Let's try x1 = 1:
2(1) + 2 = 2 + 2 = 4
The sum of the x-coordinates is 4, which is a single digit integer.
Therefore, the correct digit to enter is 4.
To find the other two vertices of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
The length of the side parallel to the x-axis is the difference between the y-coordinates of the two given points: 3 - 1 = 2.
Since the other two vertices lie on the line y = x + 2, the length of the side parallel to the x-axis is also the difference between the x-coordinates of the two unknown vertices.
Let's call the x-coordinate of one of the unknown vertices x1 and the x-coordinate of the other unknown vertex x2.
From the information above, we have:
x2 - x1 = 2
Since the sum of the x-coordinates of the other two vertices is x1 + x2, we need to find the sum of x1 and x2.
By adding x1 to both sides of the equation x2 - x1 = 2, we get:
x2 = x1 + 2
Substituting this into the sum x1 + x2, we have:
x1 + (x1 + 2) = 2x1 + 2
The sum of the x-coordinates of the other two vertices is 2x1 + 2.
Since we are looking for a single digit integer, we need to find the value of x1 that satisfies the given conditions.
From the given points (1, 3) and (5, 1), we can see that the x-coordinate of the first point is smaller than the x-coordinate of the second point.
Therefore, x1 must be less than x2.
If we try different values of x1, we can find the sum of the x-coordinates of the other two vertices.
Let's start with x1 = 0:
2(0) + 2 = 0 + 2 = 2
The sum of the x-coordinates is 2, but it is not a single digit integer.
Let's try x1 = 1:
2(1) + 2 = 2 + 2 = 4
The sum of the x-coordinates is 4, which is a single digit integer.
Therefore, the correct digit to enter is 4.
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Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer?
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Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer?.
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer?.
Solutions for Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer?, a detailed solution for Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? has been provided alongside types of Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C isCorrect answer is '4'. Can you explain this answer? theory, EduRev gives you an
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