Q28 of 47 Page 1

In Fig. 8, the vertices of ∆ABC are A(4, 6), B(1, 5) and C(7, 2). A line segment DE is drawn to intersect the sides AB and AC at D and E respectively such that . Calculate the area of ∆ADE and compare it with area of ∆ABC.


Given three coordinates A(4, 6) B(1, 5) and C(7, 2)


D divides AB in 1 : 3 and E divides AC in ratio 1 : 3


we know that the coordinates of the points P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2), internally in the ratio m : n are



So




As we know area of triangle formed by three points (x1, y1), (x2, y2) and (x3, y3)



ar(ΔABC) = 1/2 [4(5-2) + 1 (2-6) + 7 (6-5)] = 15/2





So ratio of both triangles is 1 : 16


 

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