# Lecture-4

00:00:20 NCERT Exercise 7.2 Questions 4 Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

00:09:30 NCERT Exercise 7.2 Questions 5 Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

00:16:50 NCERT Exercise 7.2 Questions 9 Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

00:22:20 NCERT Exercise 7.2 Questions 10 Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. [Hint : Area of a rhombus = 1/2(product of its diagonals)]

00:28:10 Area of triangle using coordinates of vertices

00:30:30 NCERT Exercise 7.3 Questions 1 Find the area of the triangle whose vertices are : (i) (2, 3), (–1, 0), (2, – 4) (ii) (–5, –1), (3, –5), (5, 2)

00:34:30 Proving points are collinear using area of triangle

00:37:00 NCERT Exercise 7.3 Questions 2 In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, –2), (5, 1), (3, k) (ii) (8, 1), (k, – 4), (2, –5)

00:42:00 NCERT Exercise 7.3 Questions 3 Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

00:49:00 NCERT Exercise 7.3 Questions 4 Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3).

00:54:50 NCERT Exercise 7.3 Questions 5 You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ ABC whose vertices are A(4, – 6), B(3, –2) and C(5, 2).