Q3 of 49 Page 184

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 of the area of the given triangle.

1 sq. unit; 1 : 4

⇒ Let A(0,-1),B(2,1),C(0,3)


So midpoints of AB and BC and CD


⇒ Midpoint formula



⇒ For AB =


AB =


AB =


⇒ For BC


BC =


BC =


BC =


⇒ For AC


AC =


AC =


AC =


(1,0)(1,2)(0,1)


Area ΔXYZ =


=


=


=


= 1 sq cm


⇒ Let A(0,-1),B(2,1),C(0,3)


⇒ Area ΔABC =


=


=


=


= 4 sq cm


∴ Ratio of Area of triangles is 1:4


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