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Assertion & Reason Test: Coordinate Geometry - 1


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Assertion & Reason Test: Coordinate Geometry - 1 - 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 (A): The ordinate of a point A on y-axis is 5 and B has coordinates (–3, 1). Then the length of AB is 5 units.

Reason (R): The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, –4).

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 1 In case of assertion

Here, A → (0 , 5) and B → (– 3 , 1)

= 5 units

∴ Assertion is correct.

In case of reason: If A (2, 7) lies on perpendicular bisector of P (6, 5) and Q (0, –4), then

AP = AQ

∴ By using Distance Formula,

As, AP ≠ AQ

Therefore, A does not lie on the perpendicular bisector of PQ.

∴ Reason is incorrect.

Hence, assertion is correct but reason is incorrect.

Assertion & Reason Test: Coordinate Geometry - 1 - 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 area of the triangle with vertices (-5 , -1), (3, -5), (5, 2), is 32 square units.Reason : The point (x, y) divides the line segment joining the points (x1, y1) and (x2, y2) in the ratio k : 1 externally then

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 2

and section formula (externally), we have

Assertion & Reason Test: Coordinate Geometry - 1 - 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 co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2 is (2, -3) 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 - 1 - Question 3 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 = -5, y1 = 11, x2 = 4, y2 = -7, m1 = 7, m2 = 2

So, Assertion is also correct

Assertion & Reason Test: Coordinate Geometry - 1 - 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 (A): △ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to △DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).

Reason (R): A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 4 In case of assertion: By using Distance Formula,

∴ Distance between A (-2, 0) and B (2, 0),

[∵ distance between the points (x1, y1) and (x2, y2)

Similarly, distance between B (2, 0) and C (0, 2),

In △ABC, distance between C (0, 2) and A (-2, 0),

Distance between F (0, 4) and D (–4, 0),

Distance between F (0, 4) and E (4, 0),

and distance between E (4, 0) and D (–4, 0),

Here, we see that sides of DABC and DFDE are proportional.

Therefore, by SSS similarity rule, both the triangles are similar.

∴ Assertion is correct.

In case of reason: Point Q (6, 8) will lie outside the circle if its distance from the centre of circle is greater than the radius of the circle.

Distance between centre O (0, 0) and P (5, 0),

As, point P lies at the circle, therefore, OP = Radius of circle.

Distance between centre O (0, 0) and Q (6, 8),

As OQ > OP, therefore, point Q (6, 8) lies outside of the circle.

∴ Reason is correct.

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Coordinate Geometry - 1 - 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 points (k, 2 -2k), (- k+ 1,2k) and (- 4 - k, 6 - 2k) are collinear if k = 1/2.

Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 5 Consider the given points.

(−k + 1, 2k), (k, 2 − 2k),(−4 −k, 6 − 2k)

Since, these points are collinear. Therefore the area of triangle formed by the triangle formed by the points will be zero.

Therefore,

(−k + 1)(2 − 2k − 6 + 2k) + k(6 − 2k − 2k) + (−4 − k)(2k − 2 + 2k) = 0

(−k + 1)(−4) + k(6 − 4k) + (−4 − k)(4k − 2) = 0

4k − 4 + 6k − 4k2 − 16k + 8 − 4k2 + 2k = 0

−2k2 − k + 1 = 0

2k2 + k − 1 = 0

2k2 + 2k − k − 1 = 0

2k(k + 1) − 1(k + 1) = 0

(k + 1)(2k − 1) = 0

k = −1 or k = 1/2.​

Assertion & Reason Test: Coordinate Geometry - 1 - 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 : If the points A(4, 3) and B(x, 5) lies on a circle with the centre O(2,3) then the value of x is 2.

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 - 1 - Question 6 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.

Given, the points A (4,3) and B (x, 5) lie on a circle with center O(2,3).

Then OA = OB ⇒(OA)2 = (OB)2

⇒ (4 – 2)2 + (3 – 3)2 = (x – 2)2 + (5 – 3)2

⇒ (2)2 +(0)2 = (x – 2)2 + (2)2 ⇒ 4 = (x – 2)2 + 4 ⇒(x – 2)2 = 0

⇒ x – 2 = 0 ⇒ x = 2

So, Assertion is correct

Assertion & Reason Test: Coordinate Geometry - 1 - 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 (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.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 7 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.

Assertion & Reason Test: Coordinate Geometry - 1 - 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 : Centroid of a triangle formed by the points (a, b) (b, c), and (c, a) is at origin, Then a + b + c = 0 .

Reason : Centroid of a △ABC with vertices A (x1, y1), B(x2, y2) and C (x3, y3) is given by

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 8 Centroid of a triangle with vertices (a, b) (b, c), and (c, a) is

a + b + c = 0

Assertion & Reason Test: Coordinate Geometry - 1 - 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 : The possible values of x for which the distance between the points A(x, -1) and B(5, 3) is 5 units are 2 and 8.

Reason : Distance between two given points A(x1, y1) and B(x2, y2) is given by,

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 9 We know that the Distance between two given points A(x1, y1) and B(x2, y2) is given by,

So, Reason is correct.

Now, AB = 5 ⇒ AB2 = 25

⇒ (x – 5)2 + (-1 - 3)2 = 25

⇒ (x – 5)2 = 25 – 16 = 9

⇒ x – 5 = ±3

⇒ x = 5 ± 3

⇒ x = 2, 8

So, Assertion is also correct

Assertion & Reason Test: Coordinate Geometry - 1 - 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 : Mid-point of a line segment divides line in the ratio 1 : 1.

Reason : If area of triangle is zero that means points are collinear.

Detailed Solution for Assertion & Reason Test: Coordinate Geometry - 1 - Question 10 Let us assume that point B divides the line AC in the ratio k : 1

Let(x1, y1, z1) = (0, 0, 0)

(x, y ,z) = (2, −3, 3)

(x2, y2, z2) = (−2, 3, −3)

By section formula:

x = m1 + m2 m1 x 2 + m2 x 1

⇒ 2 = k + 1 k.(−2) + 1.(0)

⇒ k = 4 − 1 on neglecting the negative sign

we get, therefore ratio is 1:4.

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