1. Find the equation of the straight line joining the point of intersection of 3x - y + 9 = 0 and
2y + x - 4 = 0 to the point of intersection of 2x + y = 4 and 2y = x + 3.

2. The vertices of a triangle ABC are A (-3, 3), B (-1, -4), and C (5, -2). M and N are the midpoints of AB and AC. Show that MN is parallel to BC and

.

3. Find the equation of the line parallel to the Y axis and passing through the point of intersection of 3x - 4y - 9 = 0 and x - 4y - 2 = 0.

4. Find the orthocenter of the triangle whose vertices are (-2, 1), (-1, -4), and (0, -5).

5. Prove that the line segments joining the mid points of the adjacent sides of a rhombus form a rectangle.

6. ABCD is a trapezium with AB || CD. The diagonals AC and BD intersect at E. If
Δ AED ||| Δ BEC, prove that AD = BC.

7. Two circles intersect each other internally at P. If ACP and BDP are the lines meeting the two circles at A, B and C, D respectively, prove that

.

8. Show that

.

9. If A = 30°, and B = 60°, verify that
(i) sin(A + B) = sin A cos B + cos A sin B
(ii) cos(A + B) = cos A cos B - sinA sin B.

10. From the top of a building 60 meters high, the angle of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. Find the height of the tower.