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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 : The point (1, 6) divides the line segment joining the points (3, 10) and (6, 8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear if AB + BC = AC
So, Reason is correct.
Let the ratio is k : 1. Here, x_{1} = 3, y_{1} = 10, x_{2} = 6, y_{2} = 8, x = 1, y = 6
Now, ycoordinate
⇒ 8k + 10 = 6k + 6
⇒ 10 – 6 = 6k + 8k
⇒ 14k = 4
⇒ k = 4/14 = 2/7
So, Assertion is correct
But reason (R) is not the correct explanation of assertion (A).
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The point (1, 6) divides the line segment joining the points (3, 10) and (6, 8) in the ratio 2 :7 internally.
Reason : Three points A,B and C are collinear if area of △ ABC = 0 .
 k 1 = 6k 3
7k = 2
k = 2/7
Ratio be 2 :7 internally.
Also, if ar(△ ABC) = 0
A,B and C all these points are collinear.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The value of y is 6, for which the distance between the points P(2, 3) and Q(10, y) is 10.
Reason : Distance between two given points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by,
So, Reason is correct.
Now, PQ = 10 ⇒ PQ^{2} = 100
⇒ (10 – 2)^{2} + (y + 3)^{2} = 100
⇒ (y + 3)^{2} = 100 – 64 = 36
⇒ y + 3 = ±6
⇒ y = 3 ± 6 ⇒ y = 3, 9
So, Assertion is not correct
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.
LHS = rational
RHS = irrational
Hence, (x_{1}, y_{1}) (x_{2}, y_{2}) and (x_{3}, y_{3}) cannot be all rational.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The point (0, 4) lies on y axis.
Reason : The x coordinate on the point on y axis is zero.
So, Reason is correct.
The x coordinate of the point (0, 4) is zero.
So, Point (0, 4) lies on y axis.
So, Assertion is also correct
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The value of y is 6, for which the distance between the points P(2, 3) and Q(10, y) is 10.
Reason : Distance between two given points A (x_{1}, y_{1}) and B(x_{2}, y_{2}) is given 6,
PQ = 10
PQ^{2} = 100
(10  2)^{2} + (y + 3)^{2} = 100
(y + 3)^{2} = 100  64 = 36
y + 3 = + 6
y =  3 + 6
y = 3, 9
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : C is the midpoint of PQ, if P is (4, x), C is (y, 1) and Q is ( 2, 4), then x and y respectively are 6 and 1.
Reason : The midpoint of the line segment joining the points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is
So, Reason is correct.
Since, C(y, 1) is the midpoint of P(4, x) and Q( 2, 4).
⇒ x = 6
So, Assertion is correct
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The point (0, 4) lies on y axis.
Reason : The x coordinate on the point on y axis is zero.
Point (0, 4) lies on y axis.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : Ratio in which the line 3x + 4y = 7 divides the line segment joining the points (1, 2) and ( 2, 1) is 3 : 5Reason : The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m2_{ }is
So, Reason is correct.
Let the ratio is k : 1.
Here, x_{1} = 1, y_{1} = 2, x_{2} = 2, y_{2} = 1, m_{1} = k, m_{2} = 1
Now, 3x + 4y = 7
⇒ 7k + 2k = 11 – 7 ⇒ 9k = 4 ⇒ k = 4/9
So, Assertion is not correct
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion: The point which divides the line joining the points A(1, 2) and B( 1, 1) internally in the ratio 1: 2 is
Reason : The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m_{2 }is
We know that the coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m_{2} is
So, Reason is correct.
Here, x_{1} = 1, y_{1} = 2, x_{2} = 1, y_{2} = 1, m_{1} = 1, m_{2} = 2
So, Assertion is correct.
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