(1) Find the area of the triangle formed by the points.
(i) (0, 0) (3, 0) and (0, 2)
(ii) (5, 2) (3, -5) and (-5, -1)
(iii) (4, -5) (4, 5) and (-1, -6)
(2) Vertices of the triangle taken in order and their areas are given below. In each of the following find the value of a.
(i) (0, 0),(4, a) and (6, 4) and its area is 17 sq.units
(ii) (a, a) , (4, 5) and (6, -1) and its area is 9 sq.units
(iii) (a, -3),(3, a) and (-1, 5) and its area is 12 sq.units
(3) Determine if the following set of points are collinear or not.
(i) (4, 3) (1, 2) and (-2, 1)
(ii) (-2, -2) (-6, -2) and (-2, 2)
(iii) (-3/2, 3) (6, -2) and (-3, 4)
(4) In each of the following, find the value of k for which the given points are collinear.
(i) (k, -1) ( 2, 1) and (4, 5)
(ii) (2, -5) ( 3 ,-4) and (9, k)
(iii) (k, k) (2 ,3) and (4, -1)
(5) If the three points (h, 0) (a, b) and (0, k) lie on a straight line, then using the area of the triangle formula show that (a/h) + (b/k) = 1,where h, k ≠ 0
(6) Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are (0, -1) (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
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