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Assertion & Reason Test: Coordinate Geometry - 2


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Assertion & Reason Test: Coordinate Geometry - 2 - Question 1

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

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 1 We know that the three points A,B and C are collinear if AB + BC = AC

So, Reason is correct.

Let the ratio is k : 1. Here, x1 = -3, y1 = 10, x2 = 6, y2 = -8, x = -1, y = 6

Now, y-coordinate

⇒ -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).

Assertion & Reason Test: Coordinate Geometry - 2 - Question 2

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 .

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 2 Using section formula, we have

- 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.

Assertion & Reason Test: Coordinate Geometry - 2 - Question 3

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(x1, y1) and B(x2, y2) is given by,

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 3 We know that the Distance between two given points A(x1, y1) and B(x2, y2) is given by,

So, Reason is correct.

Now, PQ = 10 ⇒ PQ2 = 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

Assertion & Reason Test: Coordinate Geometry - 2 - Question 4

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.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 4

LHS = rational

RHS = irrational

Hence, (x1, y1) (x2, y2) and (x3, y3) cannot be all rational.

Assertion & Reason Test: Coordinate Geometry - 2 - Question 5

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 co-ordinate on the point on y -axis is zero.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 5 We know that the if the point lies on y-axis, its x-coordinate is 0.

So, Reason is correct.

The x co-ordinate of the point (0, 4) is zero.

So, Point (0, 4) lies on y -axis.

So, Assertion is also correct

Assertion & Reason Test: Coordinate Geometry - 2 - Question 6

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 (x1, y1) and B(x2, y2) is given 6,

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 6

PQ = 10

PQ2 = 100

(10 - 2)2 + (y + 3)2 = 100

(y + 3)2 = 100 - 64 = 36

y + 3 = + 6

y = - 3 + 6

y = 3, -9

Assertion & Reason Test: Coordinate Geometry - 2 - Question 7

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 mid-point 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 mid-point of the line segment joining the points P(x1, y1) and Q(x2, y2) is

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 7 We know that the mid-point of the line segment joining the points P(x1, y1) and Q(x2, y2) is

So, Reason is correct.

Since, C(y,- 1) is the mid-point of P(4, x) and Q(- 2, 4).

⇒ x = -6

So, Assertion is correct

Assertion & Reason Test: Coordinate Geometry - 2 - Question 8

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 co-ordinate on the point on y -axis is zero.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 8 The x co-ordinate of the point (0, 4) is zero.

Point (0, 4) lies on y -axis.

Assertion & Reason Test: Coordinate Geometry - 2 - Question 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 : 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(x1, y1) and B(x2, y2) in the ratio m1 : m2 is

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 9 We know that the coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m1 : m2 is

So, Reason is correct.

Let the ratio is k : 1.

Here, x1 = 1, y1 = 2, x2 = -2, y2 = 1, m1 = k, m2 = 1

Now, 3x + 4y = 7

⇒ 7k + 2k = 11 – 7 ⇒ 9k = 4 ⇒ k = 4/9

So, Assertion is not correct

Assertion & Reason Test: Coordinate Geometry - 2 - Question 10

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(x1, y1) and B(x2, y2) in the ratio m1 : m2 is

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 2 - Question 10

We know that the coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m1 : m2 is

So, Reason is correct.

Here, x1 = 1, y1 = 2, x2 = -1, y2 = 1, m1 = 1, m2 = 2

So, Assertion is correct.

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