Internal Division

Q. A straight line through the origin O meets the parallel lines 4x+2y = 9 and 2x+y+ 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in ratio

1. 1:2
2. 3:4
3. 2:1
4. 4:3

Q.

If A (-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle. Median through(-1, 8) intersect line segment BC at D. Find the co-ordinates of point D.

1. 

2. 

3. 

4. 

Q. In the given figure, if 𝐴𝐵 || 𝑅𝑄, 𝑃𝐴 = 3𝑥+6, 𝑃𝑅 = 6𝑥, 𝑃𝐵 = 𝑥+2, and 𝑃𝑄 = 4𝑥+3 with 𝑥 < 0, then find the value of 𝑥.

Q. Equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point, is

1. 9x+20y+96=0
2. 20x+9y+96=0
3. 9x-20y+96=0
4. None of these

Q. The point A divides the join of P(-5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of $\Delta ABC$ where B is (1, 5) and C is (7, -2) is equal to 2 units.

1. undefined
2. undefined
3. undefined
4. undefined