F.3數學題 ..help ~

2009-06-07 12:07 am
D and E are the points on AB and AC respectively .
the ratio of the areas of triangle ADE and triangle ABC is 4:25
and BC//DE


[img]http://2uploadhk.com/view/36944/06062009286.jpg[/img]

回答 (1)

2009-06-07 12:18 am
✔ 最佳答案
a)
Since the area of triangle ADE and triangle ABC is 4:25
Using (the ratio of sides)^2=the ratio of areas
(AD/AB)^2=4/25
AD/AB=2/5
AD:AB=2:5
Then AD:DB=2:3
b)
By the formula of internl point ,
D={[(-1)(3)+(2)(14)]/(2+3),[(-7)(3)+(2)(13)]/(2+3)}
D=(5,1)
AE:EC=2:3
E={[(-1)(3)+(2)(-21)]/(2+3),[(-7)(3)+(2)(-3)]/(2+3)}
E=(-9,-5.4)


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