Internal Division

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. $(\frac{3}{2},3)$

2. $(\frac{1}{2},\frac{5}{2})$

3. $(\frac{-1}{2},\frac{-5}{2})$

4. $(-3,\frac{5}{2})$

Q. The coordinates of the point(s), which trisect(s) the line segment joining the points $(1,-2)$ and $(-3,4),$ are

1. $(0,\frac{-1}{2})$
2. $(\frac{-1}{3},0)$
3. $(-2,\frac{5}{2})$
4. $(\frac{-5}{3},2)$

Q. If coordinates of the centre and one end of a diameter of a circle are $(7,3)$ and $(5,-7)$ respectively, then the coordinates of the other end of the diameter are

1. $(6,-2)$
2. $(9,13)$
3. $(12,-4)$
4. $(-2,6)$

Q. $P$ and $Q$ are two points lying on the line joining the points $A(12,8)$ and $B(-2,6)$ such that $AP=PQ=QB.$ Then the midpoint of $PQ$ is

1. $(7,1)$
2. $(9,3)$
3. $(6,4)$
4. $(5,7)$

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. 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.

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