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**Q.1. Find the area of the triangle whose vertices are: ****(i) (2, 3), (âˆ’1, 0), (2, âˆ’4) ****(ii) (âˆ’5, âˆ’1), (3, âˆ’5), (5, 2)****Sol. **(i) Area of a triangle is given by**Q.2. In each of the following find the value of â€˜kâ€™, for which the points are collinear.****(i) (7, âˆ’2), (5, 1), (3, k) ****(ii) (8, 1), (k, âˆ’ 4), (2, âˆ’5)****Sol. **(i) For collinear points, area of triangle formed by them is zero.

Therefore, for points (7, âˆ’2) (5, 1), and (3, k), area = 0

(ii) For collinear points, area of triangle formed by them is zero

Therefore, for points (8, 1), (k, âˆ’4), and (2, âˆ’5), area = 0**Q.3. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, âˆ’1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.****Sol. **Let D, E and F are mid-points of the sides AB, BC and AC respectively.

The ratio of ar Î”DEF and ar Î”ABC is 1 : 4**Q.4. Find the area of the quadrilateral whose vertices, taken in order, are (âˆ’4, âˆ’2), (âˆ’3, âˆ’5), (3, âˆ’2) and (2, 3).****Sol.** Area of Î”ABC

The area of quadrilateral ABCD**Q.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 âˆ† ABC whose vertices are A (4, âˆ’6), B (3, âˆ’2) and C (5, 2).****Sol. **D is the mid-point of BC, then coordinates of D are

â‡’ A median of a triangle divides it into two triangles of equal areas.

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