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Coordinate Geometry
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10/06/2021 1:45 pm
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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.
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10/06/2021 1:48 pm
Let the vertices of the triangle be A (0, -1), B (2, 1), C (0, 3).
Let D, E, F be the mid-points of the sides of this triangle.
Coordinates of D, E, and F are given by
D = (0+2/2, -1+1/2 ) = (1, 0)
E = ( 0+0/2, -1+3/2 ) = (0, 1)
F = ( 0+2/2, 3+1/2 ) = (1, 2)
Area of a triangle = 1/2 × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]
Area of ΔDEF = 1/2 {1(2-1) + 1(1-0) + 0(0-2)} = 1/2 (1+1) = 1
Area of ΔABC = 1/2 [0(1-3) + 2{3-(-1)} + 0(-1-1)] = 1/2 {8} = 4
Therefore, the required ratio is 1:4.
This post was modified 4 years ago by Raavi Tiwari