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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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.
Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.
- 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 'D'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
In case of assertion: Distance between two points (x1, y1) and (x2, y2) is given as,
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where, (x1, y1) = (4, p)
(x2, y2) = (1, 0)
And, d = 5
Put the values, we have
52 = (1 − 4)2 + (0 – p)2
25 = (–3)2 + (–p)2
25 – 9 = p2
16 = p2
+4, –4 = p
∴ Assertion is incorrect.
In case of reason:
Let (x, y) be the point
Here, x1 = 7, y1 = –6, x2 = 3, y2 = 4, m = 1 and n = 2
So, the required point 
lies in IVth quadrant.
lies in IVth quadrant.∴ Reason is correct.
Hence, assertion is incorrect but reason is correct.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
In case of assertion: Distance between two points (x1, y1) and (x2, y2) is given as,
where, (x1, y1) = (4, p)
(x2, y2) = (1, 0)
And, d = 5
Put the values, we have
52 = (1 − 4)2 + (0 – p)2
25 = (–3)2 + (–p)2
25 – 9 = p2
16 = p2
+4, –4 = p
∴ Assertion is incorrect.
In case of reason:
Let (x, y) be the point
Here, x1 = 7, y1 = –6, x2 = 3, y2 = 4, m = 1 and n = 2
So, the required point lies in IVth quadrant.
∴ Reason is correct.
Hence, assertion is incorrect but reason is correct.
.
where, (x1, y1) = (4, p)
(x2, y2) = (1, 0)
And, d = 5
Put the values, we have
52 = (1 − 4)2 + (0 – p)2
25 = (–3)2 + (–p)2
25 – 9 = p2
16 = p2
+4, –4 = p
∴ Assertion is incorrect.
In case of reason:
Let (x, y) be the point
Here, x1 = 7, y1 = –6, x2 = 3, y2 = 4, m = 1 and n = 2
So, the required point lies in IVth quadrant.
∴ Reason is correct.
Hence, assertion is incorrect but reason is correct.
.
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Community Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.
Reason (R): The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally lies in the fourth quadrant.
The correct answer is option 'D' - A is false and R is true.
Explanation:
To determine whether the assertion (A) is true or false, let's consider the distance formula:
The distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the distance between the points (4, p) and (1, 0) is given as 5. Using the distance formula, we can write the equation as:
5 = sqrt((1 - 4)^2 + (0 - p)^2)
25 = (1 - 4)^2 + (0 - p)^2
25 = 9 + p^2
p^2 = 25 - 9
p^2 = 16
p = ±4
Hence, the value of p can be either 4 or -4. Therefore, assertion (A) is false.
Now let's consider the reason (R) statement. The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally can be found using the section formula.
The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of P(x, y) can be found using the following formulas:
x = (m*x2 + n*x1) / (m + n)
y = (m*y2 + n*y1) / (m + n)
In this case, m = 1 and n = 2. Substituting the given values into the formulas, we get:
x = (1*3 + 2*7) / (1 + 2) = (3 + 14) / 3 = 17 / 3
y = (1*4 + 2*(-6)) / (1 + 2) = (4 - 12) / 3 = -8 / 3
The coordinates of the point P are (17/3, -8/3). Since the x-coordinate is positive and the y-coordinate is negative, the point lies in the fourth quadrant.
Therefore, the reason (R) is true.
In conclusion, the assertion (A) is false and the reason (R) is true. Hence, the correct answer is option 'D'.
Reason (R): The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally lies in the fourth quadrant.
The correct answer is option 'D' - A is false and R is true.
Explanation:
To determine whether the assertion (A) is true or false, let's consider the distance formula:
The distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the distance between the points (4, p) and (1, 0) is given as 5. Using the distance formula, we can write the equation as:
5 = sqrt((1 - 4)^2 + (0 - p)^2)
25 = (1 - 4)^2 + (0 - p)^2
25 = 9 + p^2
p^2 = 25 - 9
p^2 = 16
p = ±4
Hence, the value of p can be either 4 or -4. Therefore, assertion (A) is false.
Now let's consider the reason (R) statement. The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally can be found using the section formula.
The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of P(x, y) can be found using the following formulas:
x = (m*x2 + n*x1) / (m + n)
y = (m*y2 + n*y1) / (m + n)
In this case, m = 1 and n = 2. Substituting the given values into the formulas, we get:
x = (1*3 + 2*7) / (1 + 2) = (3 + 14) / 3 = 17 / 3
y = (1*4 + 2*(-6)) / (1 + 2) = (4 - 12) / 3 = -8 / 3
The coordinates of the point P are (17/3, -8/3). Since the x-coordinate is positive and the y-coordinate is negative, the point lies in the fourth quadrant.
Therefore, the reason (R) is true.
In conclusion, the assertion (A) is false and the reason (R) is true. Hence, the correct answer is option 'D'.
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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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. 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 (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.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 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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