The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1 : 2 internally lies in the

1. Ist quadrant

2. IInd quadrant

3. IIIrd quadrant

4. IVth quadrant

The centroid of the triangle whose vertices are (-4, -2), (6, 2) and (4, 6) is :

1. (2, 2)

2. (2, 3)

3. (3, 3)

4. (0, -1)

Assertion (A): The point P(3, -1) divides the line segment joining the points A(1, -3) and B(6, 2) internally in the ratio 2 : 3.

Reason (R): The coordinates of the point which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂ are $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big).

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Assertion (A): If the coordinates of the mid-points of the sides AB and AC of Δ ABC are D(3, 5) and E(-3, 5) respectively, then BC = 12 units.

Reason (R): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).