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10. Coordinates Geometry
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Q7 of 184 Page 10

Find the area of a triangle ABC if the coordinates of the middle points of the sides of the triangle are (-1, - 2), (6, 1) and (3, 5).

Given: Coordinates of middle points are D(-1, -2), E(6, 1) and F(3, 5).


To find: Area of triangle ABC



Area of triangle


Now Area of triangle DEF




square units


Hence the area of ABC is square units


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6

Three vertices of a triangle are A(1, 2), B(-3, 6) and C(5, 4). If D, E, and C, respectively, show that the area of triangle ABC is four times the area of triangle DEF.

6

Find the area of the triangle formed by joining the mid-points of the sides of the triangles whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

8

The vertices of ΔABC are A(3, 0), B(0, 6) and (6, 9). A straight line DE divides AB and AC in the ratio 1:2 at D and E respectively, prove that

9

If (t, t - 2), (t + 3, t) and (t + 2, t + 2) are the vertices of a triangle, show that its area is independent of t.

Questions · 184
10. Coordinates Geometry
1 A 1 1 1 1 E 1 F 2 2 B 2 C 2 D 2 E 2 F 3 4 5 6 7 8 1 1 1 1 1 1 2 2 2 2 2 2 3 4 5 6 7 8 1 1 1 1 1 1 2 3 3 3 4 4 4 5 5 5 6 6 7 7 7 7 7 8 9 10 10 11 11 12 12 13 14 14 14 14 14 14 14 15 16 17 17 18 19 20 20 21 22 23 24 25 25 25 26 27 28 29 1 1 1 2 2 3 3 3 3 4 5 6 7 8 8 8 9 10 11 12 13 13 14 15 15 15 15 16 16 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1 1 1 1 1 1 1 1 2 2 2 2 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 15 15 15 15 16 17 18 19 20 21 22 23 24 25 26
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