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where (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) are the coordinates of vertices.
Now, area of ABC

[-1(1 - 7) + 3(7 - 5) + 5(5 - 1)]
= 16 square units.
Area of DEF

[4 (6 - 3) + 2(3 - 4) + 1(4 - 6)]

[12 - 2 - 2]
= 4 square units.
Hence area of ABC = 16 = 4 4
= 4 (area of DEF)

Exa-9-Find the coordinates of the circumcentre of the triangle whose vertices are (
8, 6 ), ( 8, - 2 ) and ( 2, - 2 ). Also find its circum-radius.

Soln:Let coordinate of circum centre be (x, y)
If O is circumcentre of ABC
Then OA = OB = OC

Squaring both sides
2
2
2
2
(x - 8) + (y - 6) = (x - 8) + (y + 2)
2
2
y - 12y +36 = y + 4y + 4
36 - 4 = 4y + 12y
32 = 16y
y = 2......... (1)
Again

Squaring both sides
2
2
2
2
(x - 8) + (y + 2) = (x - 2) + (y + 2)
2
2
x - 16x + 64 = x - 4x + 4
- 12x = - 60
x = 5 ..........(2)
Circumcentre = (5, 2)
So, circumradius

= 5 units

Exa:10-If the co-ordinates of the mid-points of the sides of a triangle are (1, 2),
(0, -1) and (2, -1). Find the co-ordinates of its vertices.
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