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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).
Reason : In equilateral triangle all the coordinates of three vertices can be rational.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'C'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
LHS = rational
RHS = irrational
Hence, (x1, y1) (x2, y2) and (x3, y3) cannot be all rational.
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Directions: In the following questions, A statement of Assertion (A) ...
Assertion: If A (2a, 4a) and B (2a, 6a) are two vertices of an equilateral triangle ABC, then the vertex C is given by (2a, a√3, 5a).
Reason: In an equilateral triangle, all the coordinates of three vertices can be rational.
Explanation:
To determine the vertex C of an equilateral triangle ABC, we need to consider the properties of equilateral triangles.
1. Properties of Equilateral Triangles:
- All sides of an equilateral triangle are equal in length.
- All angles of an equilateral triangle are equal to 60 degrees.
- The altitude of an equilateral triangle bisects the base and forms two congruent right triangles.
2. Determining the Length of AB:
The coordinates of A are (2a, 4a) and the coordinates of B are (2a, 6a).
Using the distance formula, we can find the length of AB:
AB = √((2a - 2a)^2 + (6a - 4a)^2)
= √(0 + 4a^2)
= 2a
3. Determining the Length of AC or BC:
Since ABC is an equilateral triangle, all sides are equal in length.
Therefore, AC = BC = AB = 2a.
4. Determining the Coordinate of C:
Let's assume the coordinates of C to be (x, y).
Since AB is parallel to the y-axis, the x-coordinate of point C will be the same as that of A and B, which is 2a.
To find the y-coordinate of C, we need to consider the altitude of the equilateral triangle.
The altitude divides the equilateral triangle into two congruent right triangles.
The length of the altitude can be found using the Pythagorean theorem:
(AC/2)^2 + (BC)^2 = AC^2
(2a/2)^2 + (a√3)^2 = (2a)^2
a^2 + 3a^2 = 4a^2
4a^2 = 4a^2
Therefore, the y-coordinate of C is a√3.
Thus, the coordinates of C are (2a, a√3, 5a).
Conclusion:
Both the assertion and reason are true. The reason provides a correct explanation for the assertion. In an equilateral triangle, all the coordinates of the three vertices can be rational, as demonstrated in this example.
Reason: In an equilateral triangle, all the coordinates of three vertices can be rational.
Explanation:
To determine the vertex C of an equilateral triangle ABC, we need to consider the properties of equilateral triangles.
1. Properties of Equilateral Triangles:
- All sides of an equilateral triangle are equal in length.
- All angles of an equilateral triangle are equal to 60 degrees.
- The altitude of an equilateral triangle bisects the base and forms two congruent right triangles.
2. Determining the Length of AB:
The coordinates of A are (2a, 4a) and the coordinates of B are (2a, 6a).
Using the distance formula, we can find the length of AB:
AB = √((2a - 2a)^2 + (6a - 4a)^2)
= √(0 + 4a^2)
= 2a
3. Determining the Length of AC or BC:
Since ABC is an equilateral triangle, all sides are equal in length.
Therefore, AC = BC = AB = 2a.
4. Determining the Coordinate of C:
Let's assume the coordinates of C to be (x, y).
Since AB is parallel to the y-axis, the x-coordinate of point C will be the same as that of A and B, which is 2a.
To find the y-coordinate of C, we need to consider the altitude of the equilateral triangle.
The altitude divides the equilateral triangle into two congruent right triangles.
The length of the altitude can be found using the Pythagorean theorem:
(AC/2)^2 + (BC)^2 = AC^2
(2a/2)^2 + (a√3)^2 = (2a)^2
a^2 + 3a^2 = 4a^2
4a^2 = 4a^2
Therefore, the y-coordinate of C is a√3.
Thus, the coordinates of C are (2a, a√3, 5a).
Conclusion:
Both the assertion and reason are true. The reason provides a correct explanation for the assertion. In an equilateral triangle, all the coordinates of the three vertices can be rational, as demonstrated in this example.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).Reason : In equilateral triangle all the coordinates of three vertices can be rational.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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